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). 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 , then G is super k-restricted edge connected.
@article{bwmeta1.element.doi-10_7151_dmgt_1939,
author = {Shiying Wang and Meiyu Wang and Lei Zhang},
title = {A Sufficient Condition for Graphs to Be SuperK-Restricted Edge Connected},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {537-545},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1939}
}
Shiying Wang; Meiyu Wang; Lei Zhang. A Sufficient Condition for Graphs to Be SuperK-Restricted Edge Connected. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 537-545. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1939/