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Representing groups by graphs with constant link and hypergraphs

✍ Scribed by Walter Vogler

Publisher
John Wiley and Sons
Year
1986
Tongue
English
Weight
772 KB
Volume
10
Category
Article
ISSN
0364-9024

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✦ Synopsis

A graph L is called a link graph if there is a graph G such that for each vertex of G its neighbors induce a subgraph isomorphic to L. Such a G is said to have constant link L. We prove that for any finite group r and any disconnected link graph L with at least three vertices there are infinitely many connected graphs G with constant link L and AutG = r. We look at the analogous problem for connected link graphs, namely, link graphs that are paths or have disconnected complements. Furthermore w e prove that for n, r L 2, but not n = 2 = r, any finite group can be represented by infinitely many connected r-uniform, n-regular hypergraphs of arbitrarily large girth.

πŸ“œ SIMILAR VOLUMES

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✍ Walter Vogler πŸ“‚ Article πŸ“… 1984 πŸ› John Wiley and Sons 🌐 English βš– 228 KB

## Abstract __A__ graph __L__ is called a link graph if there is a graph __G__ such that for each vertex of __G__ its neighbors induce a subgraph isomorphic to __L.__ Such a G is said to have constant link __.__L Sabidussi proved that for any finite group F and any __n__ β©Ύ 3 there are infinitely ma

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The graph G has constant link L if for each vertex x of. G the graph induced by G on the, vertices adjacent to x is isomorphic to L. For each graph L on 6 or fewer vertices w e decide whether or not there exists a graph G with constant link L. From this w e are able to list all graphs on 11 or fewer