A Note on the Immersion Number of Generalized Mycielski Graphs

Abstract

The immersion number of a graph G, denoted im(G), is the largest t such that G has a Kt-immersion. In this note we are interested in determining the immersion number of the m-Mycielskian of G, denoted µm(G). Given the immersion number of G we provide a lower bound for im(µm(G)). To do this we introduce the "distinct neighbor property" of immersions. We also include examples of classes of graphs where im(µm(G)) exceeds the lower bound. We conclude with a conjecture about im(µm(Kt)).