title: End-completely-regular and end-inverse lexicographic products of graphs.
abstract: 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.
authors.affiliation: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, Henan 471003, China.
authors.forename: Hailong
authors.identifier: 0000-0003-3250-3967
authors.initials: H
authors.lastname: Hou
authors.affiliation: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, Henan 471003, China.
authors.forename: Rui
authors.identifier: 0000-0001-6056-8480
authors.initials: R
authors.lastname: Gu
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical