Sufficient conditions for maximally edge-connected and super-edge-connected graphs depending on the clique number
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چکیده
منابع مشابه
Sufficient conditions for maximally edge-connected and super-edge-connected
Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...
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Theorem 1 was the starting point for many other suÆ ient onditions for = Æ. Lesniak [9℄ weakened the ondition Æ bn=2 to deg(u) + deg(v) n for all pairs of nonadja ent verti es u and v in G. Plesn k [10℄ showed that every graph of diameter 2 satis es = Æ and thus generalized Lesniak's result. Improvements of Plesn k's result an be found in Plesn k, Zn am [11℄ and Dankelmann, Volkmann [4℄ (see al...
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Let G be a connected graph with minimum degree δ and edgeconnectivity λ. A graph is maximally edge-connected if λ = δ, and it is superedge-connected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. In this paper, we show that a connected graph or a connected triangle-free graph is maximally edge-connected or sup...
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Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree and its in-degree . Now let D be a digraph with minimum degree and edge-connectivity If is real number, then the zeroth-order general Randic index is defined by . A digraph is maximally edge-connected if . In this paper we present sufficient condi...
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A connected graph with edge connectivity λ and minimum degree δ is called maximally edge-connected if λ = δ. A strongly connected digraph with arc connectivity λ and minimum degree δ is called maximally arc-connected if λ = δ. In this paper, some new sufficient conditions are presented for maximally edge-connected graphs and arc-connected digraphs. We only consider finite graphs (digraphs) with...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2019
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2096