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- W4240624241 abstract "For a connected graph the restricted edge-connectivity λ′(G) is defined as the minimum cardinality of an edge-cut over all edge-cuts S such that there are no isolated vertices in G–S. A graph G is said to be λ′-optimal if λ′(G) = ξ(G), where ξ(G) is the minimum edge-degree in G defined as ξ(G) = min{d(u) + d(v) − 2:uv ∈ E(G)}, d(u) denoting the degree of a vertex u. A. Hellwig and L. Volkmann [Sufficient conditions for λ′-optimality in graphs of diameter 2, Discrete Math 283 (2004), 113–120] gave a sufficient condition for λ′-optimality in graphs of diameter 2. In this paper, we generalize this condition in graphs of diameter g − 1, g being the girth of the graph, and show that a graph G with diameter at most g − 2 is λ′-optimal. © 2006 Wiley Periodicals, Inc. J Graph Theory 52: 73–86, 2006" @default.
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- W4240624241 date "2006-01-01" @default.
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- W4240624241 title "Sufficient conditions for λ′-optimality in graphs with girthg" @default.
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- W4240624241 doi "https://doi.org/10.1002/jgt.20150" @default.
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