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Regular graphs with given girth pair

✍ Scribed by Frank Harary; Peter Kovács

Publisher
John Wiley and Sons
Year
1983
Tongue
English
Weight
453 KB
Volume
7
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. The existence of regular graphs with given degree and girth pair is proved and simple bounds for their smallest order are developed. Several infinite classes of such graphs are constructed and it is proved that two of these families consist of smallest graphs.

📜 SIMILAR VOLUMES

A lower bound on the order of regular gr
A lower bound on the order of regular graphs with given girth pair
✍ C. Balbuena; T. Jiang; Y. Lin; X. Marcote; M. Miller 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 129 KB 👁 1 views

## Abstract The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. The existence of regular graphs with given degree and girth pair was proved by Harary and Kovács [Regular graphs with given girth pair, J Graph Theory 7 (1983), 209–218]. A (δ, __g__)‐cage is a small

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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

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## Abstract The odd girth of a graph __G__ gives the length of a shortest odd cycle in __G.__ Let __f(k,g)__ denote the smallest __n__ such that there exists a __k__‐regular graph of order __n__ and odd girth __g.__ The exact values of __f(k,g)__ are determined if one of the following holds: __k__

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✍ G.H. Zhang 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 496 KB

The odd girth of a graph \(G\) gives the length of a shortest odd cycle in \(G\). Let \(f(k, g)\) denote the smallest \(n\) such that there exists a \(k\)-regular graph of order \(n\) and odd girth \(g\). It is known that \(f(k, g) \geqslant k g / 2\) and that \(f(k, g)=k g / 2\) if \(k\) is even. T

On smallest regular graphs with a given
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✍ John Frederick Fink 📂 Article 📅 1985 🏛 John Wiley and Sons 🌐 English ⚖ 408 KB 👁 1 views

## Abstract For a nonempty graph, G, we define p(G) and r(G) to be respectively the minimum order and minimum degree of regularity among all connected regular graphs __H__ having a nontrivial decomposition into subgraphs isomorphic to G. By f(G), we denote the least integer t for which there is a c