Partially composed property of generalized lexicographic product graphs

Abstract

© World Scientific Publishing Company. For a vertex property P and a graph G, a set S of vertices of G is a P-set of G if S ∈ P. The maximum and minimum cardinality of a P-set of G are denoted by MP(G) and mP(G), respectively. If S is a P-set such that its cardinality equals MP(G) or mP(G), we say that S is an MP-set or mP-set of G, respectively. In this paper, we obtain such numbers of generalized lexicographic product graphs in some vertex properties.