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Attaching graphs to pseudo-similar vertices

Part of: Permutation groups Graph theory

Published online by Cambridge University Press:  09 April 2009

W. L. Kocay
W. L. Kocay
Affiliation:
Department of Computer Science University of Manitoba Winnipeg, MahitobaCanadaR3T 2N2
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Abstract

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Vertices u and v of a graph G are pseudo-similar if G – u ≅ G – v, but no automorphisms of G maps u to v. Let H be a graph with a distinguished vertex a. Denote by G(u. H) and G(v. H) the graphs obtained from G and H by identifying vertex a of H with pseudo-similar vertices u and v, respectively, of G. Is it possible for G(u.H) and G(v.H) to be isomorphic graphs? We answer this question in the affirmative by constructing graphs G for which G(u. H)≅ G(v. H).

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) 05C60: Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 20B15: Primitive groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 1 , February 1984 , pp. 53 - 58
Copyright
Copyright © Australian Mathematical Society 1984

References

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