Infinite self-interchange graphs

Abstract

Let G be an unoriented graph. Let I(G) denote the interchange graph of G. lfG = I(G), we shall say G is a selfinterchange graph (SIG). If for some positive integer m ^ 1, we have I m (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.