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Optimization problems of the third edge-connectivity of graphs

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Abstract

The third edge-connectivity λ3(G) of a graph G is defined as the minimum cardinality over all sets of edges, if any, whose deletion disconnects G and each component of the resulting graph has at least 3 vertices. An upper bound has been established for λ3(G) whenever λ3(G) is well-defined. This paper first introduces two combinatorial optimization concepts, that is, maximality and superiority, of λ3(G), and then proves the Ore type sufficient conditions for G to be maximally and super third edge-connected. These concepts and results are useful in network reliability analysis.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Wang Yingqian

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  1. Wang Yingqian
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Wang, Y. Optimization problems of the third edge-connectivity of graphs. SCI CHINA SER A 49, 791–799 (2006). https://doi.org/10.1007/s11425-006-0791-4

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  • DOI: https://doi.org/10.1007/s11425-006-0791-4

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