On maximal 3-restricted edge connectivity of regular graphs

References

• Amin , A. T. , Siegrist , K. T. and Slater , P. J. 1991 . On the nonexistence of uniformly optimal graphs for pair-connected reliability . Networks , 21 : 359 – 368 .
   Google Scholar
• Balbuena , C. , García-Vázquez , P. and Marcote , X. 2006 . Sufficient conditions for -optimality in graphs with girth g . J. Graph Theory , 52 : 73 – 86 .
   Google Scholar
• Bauer , D. , Boesch , F. , Suffel , C. and Tindell , R. 1985 . Combinatorial optimization problems in the analysis and design of probabilistic networks . Networks , 15 : 257 – 271 .
   Google Scholar
• Boesch , F. T. 1986 . On unreliability polynomials and graph connectivity in reliable network synthesis . J. Graph Theory , 10 : 339 – 352 .
   Web of Science ®Google Scholar
• Boesch , F. T. 1991 . On the existence of uniformly optimally reliable networks . Noetworks , 21 : 181 – 194 .
   Web of Science ®Google Scholar
• Bondy , J. A. and Murty , U. S.R. 1976 . Graph Theory with Application , London : Macmillan Press .
   Google Scholar
• Bonsma , P. , Ueffing , N. and Volkmann , L. 2002 . Edge-cuts leaving components of order at least three . Discrete Math. , 256 : 431 – 439 .
   Web of Science ®Google Scholar
• Esfahanian , A. H. and Hakimi , S. L. 1985 . Fault-tolerant routing in de Bruijn communication networks . IEEE Trans. Comp , c-34 ( 9 ) : 777 – 788 .
   Google Scholar
• Esfahanian , A. H. and Hakimi , S. L. 1988 . On computing a conditional edge connectivity of a graph . Inform. Proc. Lett. , 27 : 195 – 199 .
   Web of Science ®Google Scholar
• Hellwig , A. and Volkmann , L. 2004 . Sufficient conditions for -optimality in graphs of diameter 2 . Discrete Math. , 283 : 113 – 120 .
   Web of Science ®Google Scholar
• Hellwig , A. and Volkmann , L. 2008 . Maximally edge-connected and vertex-connected graphs and digraphs . Discrete Math. , 308 : 3265 – 3296 .
   Web of Science ®Google Scholar
• Hong , Y. M. , Liu , Q. H. and Zhang , Z. 2008 . Minimally restricted edge connected graphs . Appl. Math. Lett. , 21 : 820 – 823 .
   Google Scholar
• Latifi , S. 1994 . Conditional connectivity measure of large multiple processor systems . IEEE Trans. Comput. , 43 : 218 – 221 .
   Web of Science ®Google Scholar
• Li , Q. L. and Li , Q. 1998 . Reliability analysis of circulant graphs . Networks , 28 : 61 – 65 .
   Google Scholar
• Liu , Q. H. , Hong , Y. M. and Zhang , Z. 2009 . Minimally 3-restricted edge connected graphs . Discrete Appl. Math. , 157 : 685 – 695 .
   Google Scholar
• Moore , E. F. and Shannon , C. 1956 . Reliable circuits using less reliable relays (I) . J. Franklin Inst. , 262 : 191 – 208 .
   Google Scholar
• Moore , E. F. and Shannon , C. 1956 . Reliable circuits using less reliable relays (II) . J. Franklin Inst. , 262 : 281 – 297 .
   Google Scholar
• Ou , J. P. 2005 . Edge cuts leaving components of order at least m . Discrete Math. , 305 : 365 – 371 .
   Web of Science ®Google Scholar
• Ou , J. P. and Zhang , F. J. 2005 . 3-Restricted edge connectivity of vertex transitive graphs . ARS Combin. , 74 : 291 – 302 .
   Web of Science ®Google Scholar
• J.P. Ou, Ore-type condition for maximizing 3-restricted edge-connectivity of graphs, Submitted
   Google Scholar
• Ou , J. P. 2007 . A bound on 4-restricted edge connectivity of graphs . Discrete Math. , 307 : 2429 – 2437 .
   Web of Science ®Google Scholar
• Ou , J. P. , Cheng , X. H. and Wu , J. C. 2009 . On 3-Restricted edge connectivity of undirected binary Kautz graphs . Discrete Math. , 309 : 629 – 638 .
   Google Scholar
• Petingi , L. , Saccoman , J. T. and Schoppmann , L. 1996 . Uniformly least reliable graphs . Networks , 27 : 125 – 131 .
   Google Scholar
• Provan , J. S. and Ball , M. O. 1983 . The complexity of counting cuts and of computing the probability that a graph is connected . SIAM J. Comput. , 12 : 77 – 788 .
   Google Scholar
• Wang , M. and Li , Q. 2002 . Conditional edge connectivity properties, reliability comparison and transitivity of graphs . Discrete Math. , 258 : 205 – 214 .
   Web of Science ®Google Scholar
• Zhang , Z. and Yuan , J. J. 2007 . Degree conditions for restricted-edge-connectivity and isopermetric-edge-connectivity to be optimal . Discrete Math. , 307 : 293 – 298 .
   Google Scholar