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Vertex and Edge Transitive, but not 1-Transitive, Graphs

Published online by Cambridge University Press:  20 November 2018

I. Z. Bouwer
I. Z. Bouwer*
Affiliation:
University of New Brunswick, Fredericton, New Brunswick
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A (simple, undirected) graph G is vertex transitive if for any two vertices of G there is an automorphism of G that maps one to the other. Similarly, G is edge transitive if for any two edges [a, b] and [c, d] of G there is an automorphism of G such that {c, d} = {f(a), f(b)}. A 1-path of G is an ordered pair (a, b) of (distinct) vertices a and b of G, such that a and b are joined by an edge. G is 1-transitive if for any two 1-paths (a, b) and (c, d) of G there is an automorphism f of G such that c = f(a) and d = f(b). A graph is regular of valency d if each of its vertices is incident with exactly d of its edges.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 2 , June 1970 , pp. 231 - 237
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Tutte, W. T., Connectivity in graphs, Univ. of Toronto Press, Toronto, 1966.Google Scholar