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Graphs, groups and pseudo-similar vertices

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

W. L. Kocay
W. L. Kocay
Affiliation:
Department of Computer Science University of QueenslandSt. Lucia, Queensland, Australia Department of Computer Science University of ManitobaWinnipeg, ManitobaCanadaR3T 2N2
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Abstract

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Vertices u0, u1, …, uk−1 of a graph X are mutually pseudo-similar if X − u0 ≌ X − u1 ≌ … ≌ X − uk−1, but no two of the vertices are related by an automorphism of X. We describe a method for constructing graphs with a set of k≥2 mutually pseudo-similar vertices, using a group with a special subgroup. We show that in all graphs with pseudo-similar vertices, the vertices are pseudo-similar due to the action of a group on the cosets of some subgroup.

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) 05C99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 2 , October 1984 , pp. 181 - 189
Copyright
Copyright © Australian Mathematical Society 1984

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