Completely Regular Endomorphisms of Split Graphs

Abstract

In \([8]\), Weimin Li and Jianfei Chen studied split graphs such that the monoid of
all endomorphisms is regular. In this paper, we extend the study of \([11]\). We find
conditions such that regular endomorphism monoids of split graphs are completely
regular. Moreover, we find completely regular subsemigroups contained in the
monoid \(End(G)\).