A NEIGHBORHOOD UNION CONDITION FOR FRACTIONAL (k, n′,m)-CRITICAL DELETED GRAPHS
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چکیده
A graph G is called a fractional (k, n′,m)-critical deleted graph if any n′ vertices are removed from G the resulting graph is a fractional (k,m)-deleted graph. In this paper, we prove that for integers k ≥ 2, n′,m ≥ 0, n ≥ 8k + n′ + 4m− 7, and δ(G) ≥ k + n′ +m, if |NG(x) ∪NG(y)| ≥ n+ n′ 2 for each pair of non-adjacent vertices x, y of G, then G is a fractional (k, n′,m)-critical deleted graph. The bounds for neighborhood union condition, the order n and the minimum degree δ(G) of G are all sharp.
منابع مشابه
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تاریخ انتشار 2016