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Asymmetric and symmetric graphs

Published online by Cambridge University Press:  18 May 2009

E. M. Wright
E. M. Wright
Affiliation:
University of Aberdeen
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An (n, q) graph consists of n nodes and q edges, i.e. q distinct unordered pairs of different nodes, so that there are no loops or multiple edges. We write T for the number of unlabelled (n, q) graphs and F for the number of labelled (n, q) graphs. We say that a labelled graph is symmetric if there is a nonidentical permutation of its nodes which leaves the graph unaltered. We write r for the order of the automorphism group of the graph, i.e. the group of all those permutations of the nodes which leave the graph unaltered; we say that the graph is of symmetry order r. A graph which is not symmetric is called asymmetric and, for such a graph, obviously r = 1. We say that an unlabelled graph is symmetric or asymmetric according as the graph obtained by labelling its nodes is symmetric or asymmetric.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 15 , Issue 1 , March 1974, pp. 69 - 73
Copyright
Copyright © Glasgow Mathematical Journal Trust 1974

References

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