Vol. 31, No. 2, 1969

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Infinite self-interchange graphs

Benjamin L. Schwartz

Vol. 31 (1969), No. 2, 497–504

Let G be an unoriented graph. Let I(G) denote the interchange graph of G. If G = I(G), we shall say G is a self-interchange graph (SIG). If for some positive integer m 1, we have Im(G) = G, we shall say G is eventually self interchange (ESIG). This paper extends previous results to characterize all finite degree SIG’s and ESIG’s, (loops and parallel edges permitted), finite or infinite, connected or disconnected. It will be seen that when infinite graphs are considered, several earlier results change. For example, there are ESIG’s which are not SIG’s; and loop-free SIG’s which are not regular.

Mathematical Subject Classification
Primary: 05.40
Received: 23 September 1968
Revised: 6 May 1969
Published: 1 November 1969
Benjamin L. Schwartz