End-Completely-Regular and End-Inverse Lexicographic Products of Graphs

الملخص EN

A graph X is said to be End-completely-regular (resp., End-inverse) if its endomorphism monoid End( X ) is completely regular (resp., inverse).

In this paper, we will show that if X [ Y ] is End-completely-regular (resp., End-inverse), then both X and Y are End-completely-regular (resp., End-inverse).

We give several approaches to construct new End-completely-regular graphs by means of the lexicographic products of two graphs with certain conditions.

In particular, we determine the End-completely-regular and End-inverse lexicographic products of bipartite graphs.