PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 34(48), pp. 233--237 (1983)
ON THE AUTOMORPHISM GROUP OF AN INFINITE GRAPH
Aleksandar TorgasevMatematicki fakultet, Beograd, Yugoslavia
Abstract: In this paper, a specially defined automorphism group $\Gamma(G)$ of a connected countable simple infinite graph is considered. As the main result, we prove that $\Gamma(G)$ contains at most one non-trivial element. All infinite graphs with a non-trivial automorphism group are completely described. Finally, for graphs with odd, or with a small even number (2 or 4) of non-zero eignevalues, the corresponding automorphism groups are characterized.
Classification (MSC2000): 05C50
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© 2001 Mathematical Institute of the Serbian Academy of Science and Arts