Sufficient conditions for graphs to be λ'-optimal, super-edge-connected, and maximally edge-connected

Journal of Graph Theory

Volumn 48, Issue 3, 2005, Pages 228-246

  Hellwig, Angelika ^a   Volkmann, Lutz ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Edge connectivity; Edge cut; Restricted edge connectivity; Super edge connectivity

Indexed keywords

ASYMPTOTIC STABILITY; PROBABILITY; SET THEORY; THEOREM PROVING;

EDGE-CONNECTIVITY; EDGE-CUT; RESTRICTED EDGE-CONNECTIVITY; SUPER-EDGE-CONNECTIVITY;

GRAPH THEORY;

EID: 14644395517     PISSN: 03649024     EISSN: None     Source Type: Journal    
DOI: 10.1002/jgt.20053     Document Type: Article

References (27)

1. C. Balbuena and A. Carmona, On the connectivity and superconnectivity of bipartite digraphs and graphs, Ars Combin 61 (2001), 3-21.
2. F. Boesch and R. Tindell, Circulants and their connectivities, J Graph Theory 8 (1984), 487-499.
3. B. Bollobás, On graphs with equal edge-connectivity and minimum degree, Discrete Math 28 (1979), 321-323.
4. G. Chartrand, A graph-theoretic approach to a communications problem, SIAM J Appl Math 14 (1966), 778-781.
5. G. Chartrand and L. Lesniak, Graphs and digraphs, 3rd edition, Chapman & Hall, 1996.
6. P. Dankelmann and L. Volkmann, New sufficient conditions for equality of minimum degree and edge-connectivity, Ars Combin 40 (1995), 270-278.
7. P. Dankelmann and L. Volkmann, Degree sequence conditions for maximally edge-connected graphs and digraphs, J Graph Theory 26 (1997), 27-34.
8. A. -H. Esfahanian and S. L. Hakimi, On computing a conditional edge-connectivity of a graph, Inf Process Lett 27 (1988), 195-199.
9. J. Fàbrega and M. A. Fiol, Maximally connected digraphs, J Graph Theory 13 (1989), 657-668.
10. M. A. Fiol, On super-edge-connected digraphs and bipartite digraphs, J Graph Theory 16 (1992), 169-176.
11. D. L. Goldsmith and R. C. Entringer, A sufficient condition for equality of edge-connectivity and minimum degree of a graph, J Graph Theory 3 (1979), 251-255.
12. D. L. Goldsmith and A. T. White, On graphs with equal edge-connectivity and minimum degree, Discrete Math 23 (1978), 31-36.
13. A. K. Kelmans, Asymptotic formulas for the probability of k-connectedness of random graphs, Theor Probability Appl 17 (1972), 243-254.
14. S. Latifi, M. Hedge, and M. Naraghi-Pour, Conditional connectivity measures for large multiprocessor systems, IEEE Trans Computers 43 (1994), 218-222.
15. L. Lesniak, Results on the edge-connectivity of graphs, Discrete Math 8 (1974), 351-354.
16. Q. Li and Q. Li, Reliability analysis of circulant graphs, Networks 31 (1998), 61-65.
17. J. Plesník, Critical graphs of given diameter, Acta Fac Rerum Nat Univ Commenian Math 30 (1975), 71-93.
18. J. Plesník and S. Znám, On equality of edge-connectivity and minimum degree of a graph, Arch Match (Brno) 25 (1989), 19-25.
19. P. Turán, An extremal problem in graph theory, Mat-Fiz Lapok 48 (1941), 436-452.
20. N. Ueffing and L.Volkmann, Restricted edge-connectivity and minimum edge-degree, Ars Combin 66 (2003), 193-203.
21. L. Volkmann, Bemerkungen zum p-fachen Zusammenhang von Graphen, An Univ Bucuresti Mat 37 (1988), 75-79.
22. L. Volkmann, Edge-connectivity in p-partite graphs, J Graph Theory 13 (1989), 1-6.
23. L. Volkmann, Degree sequence conditions for super-edge-connected graphs and digraphs, Ars Combin 67 (2003), 237-249.
24. L. Volkmann, Degree sequence conditions for equal edge-connectivity and minimum degree, depending on the clique number, J Graph Theory 42 (2003), 234-245.
25. Y. Wang and Q. Li, Super-edge-connectivity properties of graphs with diameter 2, J Shanghai Jiaotong Univ (Chin Ed) 33(6) (1999), 646-649.
26. J. Wu and G. Guo, Fault tolerance measures for m-ary n-dimensional hypercubes based on forbidden faulty sets, IEEE Trans Computers 47 (1998), 888-893.
27. J. -M. Xu, A sufficient condition for equality of arc-connectivity and minimum degree of a digraph, Discrete Math 133 (1994), 315-318.