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Toughness and spectrum of a graph

✍ Scribed by A.E. Brouwer

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
289 KB
Volume
226-228
Category
Article
ISSN
0024-3795

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πŸ“œ SIMILAR VOLUMES

On the edge-toughness of a graph. II
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## 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 Ο‰ (__G__ ‐ __X__) components. We determine this quantity for some special classes of graphs that also gives the arboricity

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By a theorem of W.T. Tutte the toughness t(G) of a nonhamiltonian polyhedral graph G is less than or equal to $. Nonhamiltonian regular polyhedral graphs G with t(G) = ; are constructed; moreover, it is shown that the shortness exponent of the considered classes of polyhedral graphs is less than 1.

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Chen CC., K.M. Koh and Y.H. Peng, On the higher-order edge toughness of a graph, Discrete Mathematics 111 (1993) 113-123. For an integer c, 1 <c < 1 V(G) I-1, we define the cth-order edye toughness of a graph G as The objective of this paper is to study this generalized concept of edge toughness.