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SELF-COMPLEMENTARY VERTEX-TRANSITIVE GRAPHS NEED NOT BE CAYLEY GRAPHS

Published online by Cambridge University Press:  28 November 2001

CAI HENG LI  and
CHERYL E. PRAEGER
CAI HENG LI
Affiliation:
Department of Mathematics and Statistics, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia; [email protected], [email protected]
CHERYL E. PRAEGER
Affiliation:
Department of Mathematics and Statistics, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia; [email protected], [email protected]
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Abstract

A construction is given of an infinite family of finite self-complementary, vertex-transitive graphs which are not Cayley graphs. To the authors' knowledge, these are the first known examples of such graphs. The nature of the construction was suggested by a general study of the structure of self-complementary, vertex-transitive graphs. It involves the product action of a wreath product of permutation groups.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 6 , November 2001 , pp. 653 - 661
Copyright
© The London Mathematical Society 2001

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Footnotes

This work forms a part of an Australian Research Council grant project.