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A trivalent graph of girth ten

✍ Scribed by A.T Balaban

Publisher
Elsevier Science
Year
1972
Tongue
English
Weight
249 KB
Volume
12
Category
Article
ISSN
0095-8956

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πŸ“œ SIMILAR VOLUMES

A trivalent graph with 58 vertices and g
A trivalent graph with 58 vertices and girth 9
✍ N.L. Biggs; M.J. Hoare πŸ“‚ Article πŸ“… 1980 πŸ› Elsevier Science 🌐 English βš– 101 KB

A regular graph with valency k and girth g will be referred to as a (/,. ~.,, ,:\_';~,~,+ Petersen's graph is a (3, 5)-graph; indeed, it is the (unique) smallest (3. :,)-, ~,~;+ In general, the problem of finding a smallest (k, g)-graph is hard, an~ ~;-~,~: .~;;.-,~,' ~/~ is known only for a few val

A second trivalent graph with 58 vertice
A second trivalent graph with 58 vertices and girth 9
✍ C. W. Evans πŸ“‚ Article πŸ“… 1984 πŸ› John Wiley and Sons 🌐 English βš– 92 KB

## Abstract The trivalent graph of girth 9 with 58 vertices discovered by N. L. Biggs and M. J. Hoare is not the only graph of this kind.

Search for minimal trivalent cycle permu
Search for minimal trivalent cycle permutation graphs with girth nine
✍ TomaΕΎ Pisanski; John Shawe-Taylor πŸ“‚ Article πŸ“… 1981 πŸ› Elsevier Science 🌐 English βš– 151 KB

The question of the girth of cycle permutation graphs is discussed. It is demonstrated by a computer search, that there are no cycle permutation graphs with girth 9 on less than 60 vertices, and that precisely two non-isomorphic examples exist on 60 vertices.

A non-covering graph of girth six
A non-covering graph of girth six
✍ Oliver Pretzel πŸ“‚ Article πŸ“… 1987 πŸ› Elsevier Science 🌐 English βš– 228 KB

We construct a graph of girth 6 that cannot be oriented as the diagram of an ordered set and discuss the reasons why this particular construction cannot be extended to produce examples of larger girth. The problem of characterizing graphs that can be oriented as diagrams of ordered sets (or coverin