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Edge-superconnectivity of semiregular cages with odd girth

✍ Scribed by C. Balbuena; D. González-moreno; J. Salas

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
153 KB
Volume
58
Category
Article
ISSN
0028-3045

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✦ Synopsis

Abstract

A graph is said to be edge‐superconnected if each minimum edge‐cut consists of all the edges incident with some vertex of minimum degree. A graph G is said to be a
${d,d+1}$‐semiregular graph if all its vertices have degree either d or $d+1$. A smallest ${d,d+1}$‐semiregular graph G with girth g is said to be a $({d,d+1};g)$‐cage. We show that every $({d,d+1};g)$‐cage with odd girth g is edge‐superconnected. © 2011 Wiley Periodicals, Inc. NETWORKS, 2011

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## Abstract The odd girth of a graph __G__ is the length of a shortest odd cycle in __G__. Let __d__(__n, g__) denote the largest __k__ such that there exists a __k__‐regular graph of order __n__ and odd girth __g__. It is shown that __d____n, g__ ≥ 2|__n__/__g__≥ if __n__ ≥ 2__g__. As a consequenc