On connectivity of the cartesian product of two graphs. (English) Zbl 0927.05048

A graph \(G=(V,E)\) is maximum vertex-connected (maximum edge-connected) if its vertex-connectivity (edge-connectivity) equals \(\Bigl\lfloor \tfrac{2| E| }{| V| }\Bigr\rfloor \). Sufficient conditions for the cartesian product of two graphs to be maximum vertex-connected (maximum edge-connected) are given.
Reviewer: P.Horák (Safat)


05C40 Connectivity
05C75 Structural characterization of families of graphs
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[1] Yang, C.S.; Wang, J.F.; Lee, J.Y.; Boesch, F.T., Graph theoretic reliability analysis for the Boolean n-cube networks, IEEE trans. circuits systems, CAS-35, 9, 1175-1179, (1988) · Zbl 0656.94027
[2] Yang, C.S.; Wang, J.F.; Lee, J.Y.; Boesch, F.T., The number of spanning trees of the regular networks, Inter. J. comput. math., 23, 185-200, (1988) · Zbl 0683.05016
[3] Lesniak, L., Results on the edge-connectivity of graphs, Discrete math., 8, 351-354, (1974) · Zbl 0277.05123
[4] Volkmann, L., Edge-connectivity in p-partite graphs, J. graph theory, 13, 1, 1-6, (1989) · Zbl 0800.05008
[5] Boland, J.W.; Ringeisen, R.D., On super i-connected graphs, Networks, 24, 225-232, (1994) · Zbl 0805.05047
[6] Fàbrega, J.; Fiol, M.A., Maximally connected digraphs, J. graph theory, 13, 657-668, (1989) · Zbl 0688.05029
[7] Soneoka, T.; Nakada, H.; Imase, M., Sufficient conditions for maximally connected dense graphs, Discrete math., 63, 53-66, (1987) · Zbl 0609.05050
[8] Fiol, M.A., The super connectivity of large digraphs and graphs, Discrete math., 124, 67-78, (1994) · Zbl 0791.05068
[9] Fiol, M.A., On super-edge connected digraphs and bipartite digraphs, J. graph theory, 16, 6, 545-555, (1992) · Zbl 0769.05062
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