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- W4240198704 abstract "For a vertex v of a graph G, we denote by d(v) the degree of v. The local connectivity κ(u, v) of two vertices u and v in a graph G is the maximum number of internally disjoint u –v paths in G, and the connectivity of G is defined as κ(G)=min{κ(u, v)|u, v∈V(G)}. Clearly, κ(u, v)⩽min{d(u), d(v)} for all pairs u and v of vertices in G. Let δ(G) be the minimum degree of G. We call a graph G maximally connected when κ(G)=δ(G) and maximally local connected when for all pairs u and v of distinct vertices in G. In 2006, Hellwig and Volkmann (J Graph Theory 52 (2006), 7–14) proved that a connected graph G with given clique number ω(G)⩽p of order n(G) is maximally connected when As an extension of this result, we will show in this work that these conditions even guarantee that G is maximally local connected. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 192–197, 2010" @default.
- W4240198704 created "2022-05-12" @default.
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- W4240198704 date "2009-01-01" @default.
- W4240198704 modified "2023-09-26" @default.
- W4240198704 title "On local connectivity of graphs with given clique number" @default.
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- W4240198704 doi "https://doi.org/10.1002/jgt.20419" @default.
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