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Girth, valency, and excess

✍ Scribed by Norman Biggs

Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
235 KB
Volume
31
Category
Article
ISSN
0024-3795

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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 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

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

Graphs with valency k, edge connectivity
Graphs with valency k, edge connectivity k, chromatic index k + 1 and arbitrary girth
✍ V. Faber; J. Mycielski πŸ“‚ Article πŸ“… 1973 πŸ› Elsevier Science 🌐 English βš– 561 KB

We prove thbt if k>3 and there exists a regular graph with valency k, edge ity k and chromatic index k +l, then there exists such a graph of any girth g 14. connectiv-G=(X.E)iscalledagraph ifXisafinitesetandEc {{xr,.x2)lx1, x2 E X and x1 # x2 ). We call X the set of vertices and E the set of edges o