# Peter J Slater

## Refereed Publication List

235. On the efficiency index of a graph, J. Combinatorial Optimization 11, 10.;1007/s10878-014-9814-1 (with R. Barbosa).

234. Centroidal bases in graphs, Networks 64, 2014, 96-108 arxiv.org/abs/1406.7490 (with F. Foucaud and R. Klasing).

233. On open neighborhood locating-dominating in graphs, Elec. J. Graph Theory and  Applications 2, 2014, 87-98 (with M. Chellali, N. J. Rad and S. Seo

232. OLD trees with maximum degree three, Utilitas Mathematica 94,2014, 361-380  (with Suk Seo).

231. Few compare to the Great Roman Empire, Cong. Num. 217, 2013, 129-136  (with S. T. Hedetniemi, R. R. Rubacalba, and M. Walsh).

230. Open Locating-Dominating Interpolation for Trees, Cong. Num. 215, 2013, 145-152 (with S. Seo).

229. A framework for faults in detectors within network monitoring systems, WSEAS Trans. Math. 12, 2013, 911-916.

228. Uniqueness of vertex magic constants, SIAM J. DM 27, 2013, 708-716 (with Allen O'Neal).

227. Some new results on set-graceful and set-sequential graphs, J. Comb. Info.and Sys. Sci. 37, 2012, 229-239, (with B.D. Acharya, K. A. Germina and K. Abhishek).

226. Graphical parameters for classes of tumbling block graphs, Cong. Num. 213, 2012, 155-168 (with S. Seo).

225. Liar's domination in ladders, Cong. Num. 212, 2012, 45-56 (with T. W. Haynes and C. Stirling).

224. On efficient dominating sets in simplicial graphs, J. Comb. Math. Comb. Comp. 81, 2012, 129-134 (with R. Barbosa).

223. Local degree sequence bounds for graphical parameters, Bull. Inst. Comb. Appl. 66, 2012, 49-56.

222. Open neighborhood locating-dominating for grid-like graphs, Bull. Inst. Comb. Appl. 65, 2012, 89-100 (with S. Seo).

221. An introduction to closed/open neighborhood sums:   minimax, maximin, and spread, Math.Comp. Sci. 5, 2011, 69-80, (with F.A. O'Neal).

220. How provably graceful are the trees?, J. Indo. Math.Soc, 2011, 133-136.

219. An introduction to distance D magic graphs, J. Indo. Math.Soc., 2011, 89-107 (with F. A. O'Neal).

218. The connected hub number and the connected domination number, Networks 58, 2011, 232-237 (with P. Johnson and M. Walsh).

217. Colored-independence is NP-complete for paths, J. Comb. Math. Comb. Comp 77, 2011, 227-241 (with A. Sinko).

216. The minimax, maximin and spread values for open neighborhood sums for 2-regular graphs, Congr. Num. 208, 2011, 19-32 (with F.A. O'Neal).

215. The graph distance game, AKCE Int. J. Graphs Combin. 8, 2011, 85-96 (with W. Goddard, A. Sinko and H. Xu).

214. Distance independence in graphs, Discuss. Math. Graph Theory 31, 2011, 397-409 (with J.L. Sewell).

213. Open neighborhood locating-domination for infinite cylinders, Proc. 40th ACM SE 11, 2011, 334-335 (with S. Seo).

212. Open neighborhood locating-dominating in trees, Discrete App. Math. 159, 2011, 484-489 (with S. Seo).

211. Locating mobile intruders using dominating sets, J. Comb. Math. Comb. Comp. 74, 2010, 253-267 (with J.L. Sewell).

210. On locating-dominating in graphs, Discuss. Math. Graph Theory 30, 2010, 223-235 (with M. Chellali and M. Mimouni).

209. Open neighborhood locating-dominating sets, Australasian J. Comb. 46, 2010, 109-119 (with S. Seo).

208. Set-sized (1, 3)-domination for trees, Cong. Num. 196, 2009, 203-213 (with M. Roden-Bowie).

207. Liar's domination in graphs, Disc. Math. 309, 2009, 5884-5890 (with M. Roden-Bowie).

206. Liar's domination, Networks 54, 2009, 70-74.

205. Minimax open and closed neighborhood sums, AKCE J. Graphs Combin. 6. 2009, 183-190 (with A. Schneider).

204. Colored and proper colored domination, Bull. Inst. Comb. Appl. 55, 2009, 33-45 (wtih S. Seo).

203. Colored-domination is NP-complete for paths, Proc. Internat. Conf. Math. and Comp. Sci, Chennai, India, 2008, 30-37.

202. Disjoint dominating sets in graphs, Ramanujan Math Soc. J. (Proc. ICDM 2006), 2008, 87-100 (with S.M. Hedetniemi, S.T. Hedetniemi, R. Laskar, and L. Markus)

201. Liar's domination and the domination continuum, Cong. Num. 190 77-85 64, 2008, 65-78 (with M. Roden).

200. Some results on acquisition numbers, JCMCC 64, 2008, 65--78 (with Y. Wang).

199. Irredundant colorings of graphs, Bull. Inst. Comb. Appl. 54, 2008, 103--121 (wth T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi, and A.A. McRae).

198. Queens' domination using border squares and (A, B)-restricted domination, Disc. Math. 308, 2008, 4822-4828 (with A. Sinko).

197. Fault-tolerant metric dimension of graphs, Proc. Internat. Conf. Convexity in Discrete Structures, Ramanujan Math. Society Lecture Notes 5, 2008, 81-85 (with C. Hernando, M.Mora, and D.R. Wood).

196. Roman dominating influence parameters, Discrete Math. 307, 2007, 3194-3200 (with R. Rubalcaba)

195. Efficient (j,k) domination, Discuss. Math. Graph Theory 27, 409--423 (with R. Rubalcaba).

194. Colored problems in graphs, AKCE Int. J. Graphs Comb. 4 (2007) 191--196.

193. Competition parameters of a graph, AKCE Int. J. Graphs Comb. 4 (2007) 183--190 (with A. Sinko).

192. Domination in discrete structures--new directions, AKCE Int. J. Graphs Comb. 4 (2007) 113--115 (with B.D. Acharya and S. Arumugam).

191. Minimax neighborhood sums, Congr. Numer. 188, 2007, 183-190 (with A. Schneider).

190. Second player optimal graphs for competition problems, GTNNY LII, 2007, 13--20 (with S.J. Seo).

189. A note on obtaining k dominating sets from a k-dominating function on a tree, Bull. Inst. Comb. Appl. 51 (2007) 47--54 (with R.R. Rubalcaba).

188. The complementary product of two graphs, Bull. Inst. Comb. Appl. 51 (2007) 21--30 (with T.W. Haynes and L.C. van der Merwe).

187. An introduction to competition-directed-cycle numbers of graphs, Congr. Numer. 179 (2006) 33--47.

186. PUERMETD, RAGDDENE, summarily deranged, Congr. Numer. 180 (2006) 109--113.

185. Efficient domination in knights graphs, AKCE Int. J. Graphs Comb. 3 (2006) 193--204 (with A. Sinko).

184. A survey on graphs which have equal domination and closed neighborhood packing numbers, AKCE Int. J. Graphs Comb. 3 (2006) 93--114 (with R.R. Rubalcaba and A. Schneider).

183. Differentials in graphs, Util. Math. 69 (2006) 43--54 (with J.L. Mashburn, T.W. Haynes, S.M. Hedetniemi, and S.T. Hedetniemi).

182. An introduction to proper-coupled-domination in graphs, ACM-SE (2006) 265--270 (with S.J. Seo).

181. Competition-reachability of a Graph, Discrete Math. 306 (2006) 580--590 (with S.J. Seo)

180. An introduction to influence parameters for chessboard graphs, Congr. Numer. 172 (2005) 15--27 (with A. Sinko).

179. An introduction to colored-independence in graphs, Congr. Numer. 174 (2005) 33--40

178. Trees with equal domination and paired-domination numbers, Ars Comb. 76 (2005) 169--175 (with T.W. Haynes and M.A. Henning).

177. An introduction to maximum sum permutations of graphs, Ars Comb. 72 (2004) 307--310 (with S.J. Winters).

176. An introduction to competition-reachability of a graph, ACM-SE (2004) 121--125 (with S.J. Seo).

175. Colored-domination in graphs, Congr. Numer. 167 (2004) 149--159 (with S.J. Seo).

174. The competitive-acquisition numbers of paths, Congr. Numer. 167 (2004) 33--43 (with Y. Wang).

173. Strong equality of domination parameters in trees, Discrete Math. 260 (2003) 77--87 (with T.W. Haynes and M.A. Henning).

172. H-domination in graphs, Discrete Math. 272 (2003) 97--105 (with K.M. Koh and B.B. Bock).

171. Distance and connectivity measures in permutation graphs, Discrete Math. 271 (2003) 61--70 (with W. Goddard and M. Raines).

170. Graphs of order n with locating-chromatic number n - 1, Discrete Math. 269 (2003) 65--79 (with G. Chartrand, D. Erwin, M.A. Henning and P. Zhang).

169. Distance-location numbers of graphs, Util. Math. 63 (2003) 65-79 (with G. Chartrand, D. Erwin and P. Zhang).

168. H-forming sets in graphs, Discrete Math. 262 (2003) 159-169 (with T.W. Haynes, S.T. Hedetniemi and M.A. Henning).

167. Efficient open domination in graphs, Sci. Ser. A Math. Sci. 6 (2003) 77--84 (with H. Gavlas and K. Schultz).

166. Graph competition independence and enclaveless parameters, Congr. Numer. 154 (2002) 79--100 (with J.B. Phillips).

165. Parity dimension for graphs - a linear algebraic approach, Linear and Multilinear Algebra 50 (2002) 327-342 (with A.T. Amin and G-H. Zhang).

164. The locating-chromatic number of a graph, Bull. Inst. Comb. Appl. 36 (2002) 89--101 (with G. Chartrand, D. Erwin, M.A. Henning and P. Zhang).

163. Fault-tolerant locating-dominating sets, Discrete Math. 249 (2002) 179--189.

162. Multi-fractional domination, J. Comb. Math. and Comb. Comp. 40 (2002) 171--181 (with E. Trees).

161. Average distance in colored graphs, J. Graph Theory 38 (2001) 1--17 (with P. Dankelmann and W. Goddard).

160. Colored distance in grid graphs, Congr. Numer. 152 (2001) 65--73 (with J.B. Phillips).

159. Paired domination in grid graphs, Congr. Numer. 150 (2001) 161--172 (with K. Proffitt and T.W. Haynes).

158. An introduction to graph competition independence and enclaveless parameters, Graph Theory Notes of New York 41 (2001) 37--41 (with J.B. Phillips).

157. Strong equality of upper domination and independence in trees, Util.Math. 59 (2001) 111--124 (with T.W. Haynes and M.A. Henning).

156. The chromatic distance of a graph, Graph Theory Notes of New York 40 (2001) 8--11.

155. A generalization of domination-critical graphs, Util. Math. 58 (2000) 129--144 (with J.B. Phillips and T.W. Haynes).

154. On the minimum influence of a maximal packing, J. Comb. Math. Comb. Comp. 33 (2000) 275--288 (with J.B. Phillips).

153. Distance-k independent domination sequences, J. Comb. Math. Comb. Comp. 33 (2000) 225--237 (with O. Favaron and T.W. Haynes).

152. Bounds on the total redundance and efficiency of a graph, Ars Comb. 54 (2000) 129--138 (with W. Goddard, O. Oellermann and H. Swart).

151. A matrix partition linear programming theorem, Bull. Inst. Comb. Appl. 28 (2000) 75--84 (with E.L. Trees).

150. Minimum coverage by dominating sets in graphs, J. Comb. Math. Comb. Comp. 32 (2000) 33--50 (with C.B. Smart).

149. The Hedetniemi number of a graph, Congr. Numer. 139 (1999) 65--75.

148. Realizability of (j, t)-critical graphs for sets of values, Congr. Numer. 137 (1999) 65--75 (with T.W. Haynes and J.B. Phillips).

147. Center, median and centroid subgraphs, Networks 34 (1999) 303--311 (with C.B. Smart).

146. A survey of sequences of central subgraphs, Networks 34 (1999) 244--249.

145. MAD partitioning for grid graphs, J. Comb. Math. Comb. Comp. 31 (1999) 65--83 (withD.L.Meiers).

144. The complementation theorem, Combinatorics, Graph Theory and Algorithms, eds. Y. Alavi,D.R. Lick and A.J. Schwenk, New Issues Press, Western Michigan University, 1999, 787-797.

143. Open packing in graphs, J. Comb. Math. Comb. Comp. 29 (1999) 3--16 (with M.A. Henning).

142. Dynamic domination in graphs, Congr. Numer. 132 (1998) 183--188.

141. Paired domination in graphs, Networks 32 (1998) 199--206 (with T.W. Haynes).

140. Closed neighborhood order dominating functions, Australasian J. Comb. 17 (1998) 77--88 (with M.A. Henning).

139. Parallel knockouts in the complete graph, Amer. Math. Monthly 105 (1998) 556--558 (with D.E. Lampert).

138. Parity dimension for graphs, Discrete Math. 187 (1998) 1--17 (with A.A. Amin and L.C. Clark).

137. Efficient and excess domination in graphs, J. Comb. Math. Comb. Comp. 26 (1998) 83--95 (with F. Harary and T.W. Haynes).

136. All cycles are edge-magic, Bull. Inst. Comb. Appl. 22 (1998) 93--97 (with R. Godbold).

135. LP-duality, complementarity and generality of graphical subset problems, Domination inGraphs Advanced Topics, eds. T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Marcel-Dekker,Inc., 1998, 1-30.

134. Random walks with merging, Graph Theory Notes of New York XXXIII, 1997, 33--35.

133. Efficient coverage of edge sets in graphs, Util. Math. 51 (1997) 183--191, (with J. Dunbar,J.H. Hattingh and A. McRae).

132. The automorphism class theorem for LP-based graphical parameters, Bull. Inst. Comb. Appl. 20 (1997) 19--26.

131. Interior parameters in ir   i   ??  IR, Congr. Numer. 122 (1996) 129--143 (withD.E. Lampert).

130. Generalized domination and efficient domination in graphs, Discrete Math. 159 (1996) 1--11(with D.W. Bange, A.E. Barkauskas and L.H. Host).

129. Inequalities relating domination parameters in cubic graphs, Discrete Math. 158 (1996) 87--98(with M.A. Henning).

128. An overview of graphical weighted subset problems, Graph Theory Notes of New York XXXI,1996, 44--47.

127. All parity realizable trees, J. Comb. Math. and Comb. Comp. 20 (1996) 53--63 (with A.A.Amin).

126. Generalized graph parameters: Gallai theorems 1, Bull. Inst. Comb. Appl. 17 (1996) 27--37.

125. The algorithmic complexity of signed domination in graphs, Australasian J. Comb. 12 (1995)101--112 (with J.H. Hattingh and M.A. Henning).

124. Complexity results for closed neighborhood order parameters, Congr. Numer. 112 1995,83--96 (with C.B. Smart).

123. The acquisition number of a graph, Congr. Numer. 109 (1995) 203--210 (with D.E. Lampert).

122. Paired domination and the paired-domatic number, Congr. Numer. 109 (1995) 67--72 (withT.W. Haynes).

121. On the additive bandwidth of graphs, J. Comb. Math. and Comb. Comp. 18 (1995) 129--144(with M.E. Bascunan, R.C. Brigham, R.M. Caron, S. Ruiz and R.P. Vitray)

120. Signed domination in graphs, Graph Theory, Combinatorics and Applications, Eds. Y.Alaviand A.Schwenk, John Wiley and Sons, Inc., 1995, 311-321 (with J. Dunbar, S.T. Hedetniemiand M.A. Henning).

119. Locating dominating sets and locating-dominating sets, Graph Theory, Combinatorics andApplications, Eds. Y. Alavi and A. Schwenk, John Wiley and Sons, Inc., 1995, 1073-1079.

118. Packing into closed neighborhoods, Bull. Inst. Comb. Appl. 13 (1995) 23--33.

117. On maximum sum problems in graphs, Congr. Numer. 101 (1994) 87--95 (with A.T. Amin).

116. A recurrence template for several parameters in series-parallel graphs, Discrete Appl. Math.54 (1994) 151--168 (with D.L. Grinstead).

115. Three-valued k-neighborhood domination in graphs, Australasian J. of Combinatorics 9(1994) 233--242 (with J.H. Hattingh and M.A. Henning).

114. Efficient edge domination problems in graphs, Inf. Process. Lett. 48 (1993) 221--228 (withD.L. Grinstead, N.P. Holmes and N.A. Sherwani).

113. Maximum independent, minimally redundant sets in series-parallel graphs, Quaestiones Math-ematicae 16 (1993) 351--365 (with T.W. Johnson).

112. Maximum matching among minimum dominating sets, Ars Comb. 35A (1993) 239--249.

111. Closed neighborhood order domination and packing, Congr. Numer. 97 (1993) 33--43.

110. The expected number of pairs of connected nodes: pair-connected reliability, Mathematicaland Computer Modelling 17 (1993) 1--11 (with A.T. Amin and K.T. Siegrist).

109. On uniformly optimally reliable graphs for pair-connected reliability with vertex failures,Networks 23 (1993) 185--193 (with A.T. Amin and K.T. Siegrist).

108. A note on well-covered graphs, Annals of Discrete Math. 55 (1993) 179--182 (with V. Chvatal).

107. The optimal unicyclic graphs for pair-connected reliability, Discrete Appl. Math. 41 (1993)235--243 (with A.T. Amin and K.T. Siegrist).

106. Neighborhood domination with parity restrictions in graphs, Congr. Numer. 91 (1992) 19--31(with A.T. Amin).

105. The additive bandwidth of grids and complete bipartite graphs, Congr. Numer. 88 (1992)245--254 (with M.E. Bascunan and S.Ruiz).

104. Distinct distance sets in graphs, Discrete Math. 93 (1991) 155--165 (with R.A. Gibbs).

103. On the nonexistence of uniformly optimal graphs for pair-connected reliability, Networks 21 (1991) 359--368 (with A.T. Amin and K.T. Siegrist).

102. Minimum dominating, optimally independent vertex sets in graphs, in Graph Theory, Combinatorics and Applications (Proc. Sixth Quadrennial International Conf. on the Theory and Applications of Graphs, Western Michigan University, 1988) Vol. 2, 1991, 1061-1073 (with W.J. Selig).

101. On the minimum intersection of minimum dominating sets in series-parallel graphs, In Graph Theory, Combinatorics and Applications (Proc. Sixth Quadrennial International Conf. on the Theory and Applications of Graphs, Western Michigan University, 1988) Vol. 1, 1991, 563-584 (with D.L. Grinstead).

100. On minimum dominating sets with minimum intersection, Discrete Math. 86 (1990) 239--254 (with D.L. Grinstead) (also in Annals of Discrete Math. 48 Topics on Domination).

99. Fractional domination and fractional packing in graphs, Congr. Numer. 71 (1990) 153--172 (with D.L. Grinstead).

98. Maximum independent, minimally c-redundant sets in graphs, Congr. Numer. 74 (1990) 193--211 (with T.W. Johnson).

97. The central limit theorem and the law of large numbers for pair-connectivity in Bernoulli trees, Prob. in the Engineering and Informational Sciences, 1989, 477--491, (with A.T. Amin and K.T. Siegrist)

96. A summary of results on pair-connected reliability, Contemporary Math. 89 (1989) 145--152.

95. Dominating and reference sets in a graph, J. Math. and Phys. Sciences 22 (1988) 445--455.

94. Realization of majority preference digraphs by graphically determined voting patterns, Congr. Numer. 67 (1988) 175--186 (with T.W. Johnson).

93. Pair-connected reliability of communication networks with vertex failures, Congr. Numer. 67 (1988) 233--242 (with A.T. Amin and K.T. Siegrist).

92. Efficient dominating sets in graphs, Applications of Discrete Math. (Proc. Third Conf. on Discrete Math., Clemson, 1986), eds. R.D.Ringeisen and F.S.Roberts, SIAM, Philadelphia, 1988, 189--199 (with D.W. Bange and A.E. Barkauskas).

91. The k-processing center of a graph, Congr. Numer. 60 (1987) 199--210 (with D.L. Grinstead).

90. Efficient near-domination of grid graphs, Congr. Numer. 58 (1987) 83--92 (with D.W. Bange, A.E. Barkauskas and L. Host).

89. Exact formulas for reliability measures for various classes of graphs, Congr. Numer. 58 (1987) 43--52 (with A.T. Amin and K.T. Siegrist).

88. Pair-connected reliability of a tree and its distance degree sequences, Congr. Numer. 58 (1987) 29--42 (with A.T. Amin and K.T. Siegrist).

87. Locating-dominating sets in series-parallel networks, Proc 16th Annual Conf. on Numerical Math. and Computing, Winnipeg, Manitoba 1986, Congr. Numer. 56 (1987) 135-162 (with C.J. Colbourn and L.K. Stewart).

86. On a characterization of comparability graphs, Ars Comb. 23A (1987) 67--79 (with O. Chan and C.C. Chen).

85. Domination and location in acyclic graphs, Networks 17 (1987) 55-64.

84. Convex labelling of trees, J. Graph Theory 11 (1987) 59--70 (with S.J. Dow and D.F. Rall).

83. A linear algorithm for the cutting center of a tree, Inf. Process. Lett. 23 (1986) 317--319 (with F. Harary).

82. On k-graceful, countably infinite graphs, Discrete Math. 61 (1986) 293--303.

81. On iterated clique graphs with increasing diameters, J. Graph Theory 10 (1986) 167--171 (with C. Peyrat and D.F. Rall).

80. Minimum average distance of the vertices on a line network, Congr. Numer. 49 (1985) 215--221.

79. Graceful and sequential numberings of infinite graphs, Southeast Asian Bulletin of Mathematics 9 (1985) 15--22.

78. A linear algorithm for finding an optimal dominating subforest of a tree, Graph Theory with Applications to Algorithms and Computer Science, JohnWiley and Sons, 1985, 501--506 (with E. Lawler).

77. Packing a tree with a graph of the same size, J. Graph Theory 9 (1985) 213--216 (with S.K. Teo and H.P. Yap).

76. A note on similar edges and edge-unique line graphs, J. Comb. Theory Ser. B 38 (1985) 31--40 (with D.W. Bange and A.E. Barkauskas).

75. On transitively orientable graphs, Math. Medley 12 (1984) (with O. Chan and C.C. Chen).

74. On location-domination numbers for certain classes of graphs, Congr. Numer. 45 (1984) 97--106 (with D.F. Rall).

73. A Boolean algebraic analysis of fire protection, Annals of Discrete Math. 19 (1984), Algebraic Structures in Operations Research, 215-228 ( with B.L. Hulme and A.W. Shiver).

72. Eilerian partitionable graphs, Proc. First S.E.Asian Graph Theory Colloquium (Singapore, 1983), Lecture Notes in Math. 1073, Springer-Verlag, (1984), Open Problem Section, 331.

71. Some definitions of central structures, Proc. First S.E.Asian Graph Theory Colloquium (Singapore, 1983), Lecture Notes in Math. 1073, Springer-Verlag, (1984), 169-178.

70. Rinds of a graph, Ars Comb. 18 (1983) 173--180 ( with P.M. Gibson).

69. Graphs with unique subgraphs, Congr. Numer. 39 (1983) 107--115 (with D.W. Bange and A.E. Barkauskas).

68. On k-graceful, locally finite graphs, J. Comb. Theory Ser. B 35 (1983) 319--322.

67. A problem on decomposing graphs into trees and paths, Discrete Math. 47 (Problem Section) (1983) 135.

66. An optimal diagonal tree code, SIAM J. Alg. Disc. Methods 4 (1983) 42--49 (with S. Chaiken and A.K. Dewdney).

65. How few n-permutations contain all possible k-permutations?, Amer. Math. Monthly 90 (1983) 461.

64. Sequentially additive graphs, Discrete Math. 44 (1983) 235--241 (with D.W. Bange and A.E. Barkauskas).

63. On repeated difference sequences of a permutation of N, J. Number Theory 16 (1983) 1--5.

62. Maximal outerplane graphs and their associated trees, Rivista Di Mathematica Della Universita Di Parma 8 (1982) 27--35 (with D.W. Bange and A.E. Barkauskas).

61. Centers and medians of C(n)-trees, Util. Math. 21 (1982), 225-234 (with S.M.Hedetniemi and S.T. Hedetniemi).

60. A linear algorithm for the number of degree constrained subforests of a tree, Inf. Process. Lett. 15 (1982) 186--188.

59. On k-graceful graphs, Congr. Numer. 36 (1982) 53--57.

58. Counterexamples to Randic's conjecture on distance degree sequences for trees, J. Graph Theory 6 (1982) 89--92.

57. Locating central paths in a graph, Transportation Science 16 (1982) 1--18.

56. The origin of extended degree sequences of graphs, Congr. Numer. 33 (1981) 309--320.

55. Minimean location of different facilities on a line network, SIAM J. Algebraic and Discrete Math. 2 (1981) 411--415 (with B.L. Hulme).

54. Pairs of nonisomorphic graphs having the same path degree sequence, MATCH (Communications in Mathematical Chemistry) 12 (1981), 75--86 (with L.V. Quintas).

53. On graphs containing a given graph as center, J. Graph Theory 5 (1981) 427--434 (with F. Buckley and Z. Miller).

52. Information dissemination in trees, SIAM J. Computing 10 (1981) 692--701 (with E.J. Cockayne and S.T. Hedetniemi).

51. On the maximum number of cycles in a graph, Ars Comb. 11 (1981) 289--294 (with R.C. Entringer).

50. A note on packing two trees into K, Ars Comb. 11 (1981) 149--153 (with S.M.Hedetniemi and S.T. Hedetniemi).

49. The k-nucleus of a graph, Networks 11 (1981) 233--242.

48. Accretion centers: a generalization of branch-weight centroids, Discrete Appl. Math. 3 (1981) 187--192.

47. On locating a facility to service areas within a network, Operations Research 29 (1981) 523--531.

46. On k-sequential and other numbered graphs, Discrete Math. 34 (1981) 185-193.

45. Fibonacci numbers in tree counts for maximal outerplane and related graphs, Fibonacci Q. 19 (1981) 28--34 (with D.W. Bange and A.E. Barkauskas).

44. Centrality of paths and vertices in a graph: cores and pits, The Theory of Applications of Graphs, John Wiley and Sons, Inc., 1981, 529--542.

43. Which grids are Hamiltonian?, Congr. Numer. 29 (1980) 511--524 (with S.M. Hedetniemi and S.T. Hedetniemi).

42. Medians of arbitrary graphs, J. Graph Theory 4 (1980) 389--393.

41. A linear algorithm for a core of a tree. J. Algorithms 1 (1980) 247--258 (with C.A. Morgan).

40. Appraising the centrality of vertices in trees, Stud. Sci. Math. Hung. 12 (1980) 229--231.

39. Conservative graphs, J. Graph Theory 4 (1980) 81--91 (with D.W. Bange and A.E. Barkauskas).

38. A problem concerning restricted gray codes, Congr. Numer. 23 (1979) 918--919.

37. The generalized Peterson graphs G(n, 4) are Hamiltonian unless n = 8, Congr. Numer. 23 (1979) 861--871 (with G.J. Simmons).

36. Simply sequential and graceful graphs, Congr. Numer. 23 (1979) 155--162 (with D.W. Bange and A.E. Barkauskas).

35. Permutations of the positive integers with restrictions on the sequence of differences II, Pacific J. Math. 82 (1979) 527--531 (with W.Y.Velez).

34. Gossips and telegraphs, J. Franklin Institute 307 (1979) 353--360 (with R.C. Entringer).

33. Matchings and transversals in hypergraphs, domination and independence in trees, J. Comb. Theory Ser. B 26 (1979) 78--80 (with E.J. Cockayne and S.T. Hedetniemi).

32. Path coverings of the vertices of a tree, Discrete Math. 25 (1979) 65--74.

31. A theorem on critically 3-connected graphs, Nanta Math. 11 (1978) 141--145 (with R.C. Entringer).

30. A constructive characterization of trees with at least k disjoint maximum matchings, J. Comb. Theory 25 (1978) 326--338.

29. Critical and minimal graphs, Open problem section, Proc. Second International Conf. on Comb. Math. in N.Y.C., 1978, 577--578 (with S.B. Maurer).

28. Minimally 2-edge-connected graphs, Proc. Second International Conf. on Comb. Math. in N.Y.C., 1978, 377--382 (with S.B. Maurer).

27. Structure of the k-centra of a tree, Congr. Numer. 21 (1978) 663--670.

26. A constructive characterization of trees with two disjoint minimum dominating sets, Congr. Numer. 21 (1978) 101--112 (with D.W. Bange and A.E. Barkauskas).

25. On k-minimally, n-edge-connected graphs, Discrete Math. 24 (1978) 185--195 (with S.B. Maurer).

24. A characterization of SOFT hypergraphs, Can. Math. Bull. 21 (1978) 335--337.

23. Generating all permutations by graphical transpositions, Ars Comb. 5 (1978) 219--225.

22. Centers to centroids in graphs, J. Graph Theory 2 (1978) 209--222.

21. Soldering and point splitting, J. Comb. Theory 24 (1978) 338--343.

20. On k-critical, n-connected graphs, Discrete Math. 20 (1977) 255--262 (with S.B. Maurer).

19. Subtrees of a tree that form a Konig system, Ars Comb. 4 (1977) 271--283.

18. Using associated trees to count the spanning trees of labelled maximal outerplanar graphs, Congr. Numer. 19 (1977) 605--614 (with D.W. Bange and A.E. Barkauskas).

17. Enclaveless sets and MK-systems, J. Res. Nat. Bur. Stan. 82 (1977) 197--202.

16. A note on k-critically, n-connected graphs, Proc. Amer. Math. Soc. 66 (1977) 372--375 (with R.C. Entringer).

15. Geodetic connectivity of graphs, IEEE Trans. on Circuits and Systems 24 (1977) 460--463 (with R.C. Entringer and D.E. Jackson).

14. Permutations of the positive integers with restrictions on the sequence of differences, Pacific J. Math. 71 (1977) 193--196 (with W.Y. Vlez).

13. Fibonacci numbers in the count of spanning trees, Fibonacci Q. 15 (1977) 11--14.

12. A note on pseudointersection graphs, J. Res. Nat. Bur. Stan. 80B (1976) 441--445.

11. R-domination in graphs, J. Asso. Comp. Mach. 23 (1976) 446--450.

10. Central vertices in a graph, Congr. Numer. 17 (1976) 487--497.

9. On the optional hamiltonian-completion problem, Networks 6 (1976) 35-51, (with S.E. Goodman and S.T. Hedetniemi).

8. Maximin facility location, J. Res. Nat. Bur. Stan. 79B (1975) 107--115.

7. Generalized soldering, Proc. Fifth British Comb. Conf. (1975) 559--568.

6. Leaves of trees, Congr. Numer. 14 (1975) 549--559.

5. Advances on the hamiltonian-completion problem, J. Asso. Comp. Mach. 22 (1975) 352--360 (with S.E. Goodman and S.T. Hedetniemi).

4. Irreducible point independence numbers and independence graphs, Congr. Numer. 10 (1974) 647--660.

3. Some results on the optional and nonoptional hamiltonian-completion problem, Congr. Numer. 10 (1974) 423--448 (with S.E. Goodman and S.T. Hedetniemi).

2. A classification of 4-connected graphs, J. of Combinatorial Theory 17 (1974) 261--289.

1. Line graphs of triangleless graphs and iterated clique graphs, Graph Theory and Applications, Springer-Verlag, Berlin, 1972, 139-149 (with S.T. Hedetniemi).