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On the edge-toughness of a graph. II

✍ Scribed by Y. H. Peng; T. S. Tay

Publisher: John Wiley and Sons
Year: 1993
Tongue: English
Weight: 558 KB
Volume: 17
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190170211

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✦ Synopsis

Abstract

The edge‐toughness T~1~(G) of a graph G is defined as
equation image
where the minimum is taken over every edge‐cutset X that separates G into ω (G ‐ X) components. We determine this quantity for some special classes of graphs that also gives the arboricity of these graphs. We also give a simpler proof to the following result of Peng et al.: For any positive integers r, s satisfying r/2 < s ≤ r, there exists an infinite family of graphs such that for each graph G in the family, λ(G) = r (where λ(G) is the edge‐connectivity of G) T~1~(G) = s, and G can be factored into s spanning trees. © 1993 John Wiley & Sons, Inc.

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