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A smallest graph of girth 5 and valency 6

✍ Scribed by M O'Keefe; Pak-Ken Wong

Publisher
Elsevier Science
Year
1979
Tongue
English
Weight
309 KB
Volume
26
Category
Article
ISSN
0095-8956

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πŸ“œ SIMILAR VOLUMES

The smallest graph of girth 6 and valenc
The smallest graph of girth 6 and valency 7
✍ M. O'Keefe; P. K. Wong πŸ“‚ Article πŸ“… 1981 πŸ› John Wiley and Sons 🌐 English βš– 258 KB

## Abstract With the aid of a computer. we give a regular graph of girth 6 and valency 7, which has 90 vertices and show that this is the unique smallest graph with these properties.

On the uniqueness of the smallest graph
On the uniqueness of the smallest graph of girth 5 and valency 6
✍ Pak-Ken Wong πŸ“‚ Article πŸ“… 1979 πŸ› John Wiley and Sons 🌐 English βš– 96 KB πŸ‘ 1 views

Let G be a regular graph of girth n( 2 5 ) and valency k ( r 3 ) , that has the least possible number f(k, n ) of vertices. Although the existence of such a graph was proved by Erdos and Sachs (see Ref. 6, p. 82), only a few cases have been solved (see Refs. 2-7). Recently, O'Keefe and Wong have sho

On the smallest graphs of girth 10 and v
On the smallest graphs of girth 10 and valency 3
✍ P.K. Wong πŸ“‚ Article πŸ“… 1983 πŸ› Elsevier Science 🌐 English βš– 511 KB

Recently, O'Keefe and Wong have shown that a smallest graph of girth 10 and valency 3 (a (3,lO)-cage) must have 70 vertices. There are three non-isomorphic (3,10)-cages which have been known for some while. In this papel, it is shown that these are the only three possible (3,lO)-cages. Some of the p

The maximum valency of regular graphs wi
The maximum valency of regular graphs with given order and odd girth
✍ Guo-Hui Zhang πŸ“‚ Article πŸ“… 1992 πŸ› John Wiley and Sons 🌐 English βš– 294 KB πŸ‘ 1 views

## 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__ β‰₯ 2|__n__/__g__β‰₯ if __n__ β‰₯ 2__g__. As a consequenc