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A Sufficient Condition for Graphs to Be SuperK-Restricted Edge Connected

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Wang S., Wang M., Zhang L.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 3

537-545

For a subset S of edges in a connected graph G, S is a k-restricted edge cut if G − S is disconnected and every component of G − S has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is defined as the cardinality of a minimum k-restricted edge cut. Let ξk(G) = min{|[X, X̄]| : |X| = k, G[X] is connected}, where X̄ = V (G)\X. A graph G is super k-restricted edge connected if every minimum k-restricted edge cut of G isolates a component of order exactly k. Let k be a positive integer and let G be a graph of order ν ≥ 2k. In this paper, we show that if |N(u) ∩ N(v)| ≥ k +1 for all pairs u, v of nonadjacent vertices and [...] ξk(G)≤⌊ν2⌋+k $\xi _k (G) \le \left\lfloor {{\nu \over 2}} \right\rfloor + k$ , then G is super k-restricted edge connected.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Wang M.

1 Wang S.

1 Zhang L.

1 2017

Wyniki wyszukiwania

A Sufficient Condition for Graphs to Be SuperK-Restricted Edge Connected