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Graphs with given group and given constant link

✍ Scribed by Walter Vogler

Publisher: John Wiley and Sons
Year: 1984
Tongue: English
Weight: 228 KB
Volume: 8
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190080113

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✦ Synopsis

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 ⩾ 3 there are infinitely many n‐regular connected graphs G with Aut__G ≅ Γ. We will prove a stronger result: For any finite group Γ and any link graph L with at least one isolated vertex and at least three vertices there are infinitely many connected graphs G with constant link L and Aut__G ≅ Γ.

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