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Sufficient conditions for graphs to be λ′-optimal and super-λ′

✍ Scribed by Li Shang; Heping Zhang


Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
200 KB
Volume
49
Category
Article
ISSN
0028-3045

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📜 SIMILAR VOLUMES


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## Abstract The restricted‐edge‐connectivity of a graph __G__, denoted by λ′(__G__), is defined as the minimum cardinality over all edge‐cuts __S__ of __G__, where __G__‐__S__ contains no isolated vertices. The graph __G__ is called λ′‐optimal, if λ′(__G__) = ξ(__G__), where ξ(__G__) is the minimum

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The total chromatic number χ T (G) of graph G is the least number of colors assigned to V (G) ∪ E(G) such that no adjacent or incident elements receive the same color. In this article, we give a sufficient condition for a bipartite graph G to have χ T (G) = ∆(G) + 1.

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## Abstract Restricted edge connectivity is a more refined network reliability index than edge connectivity. For a connected graph __G__ = (__V__, __E__), an edge set __S__ ⊆ __E__ is a restricted edge cut if __G__ − __S__ is disconnected and every component of __G__ − __S__ has at least two vertic