Forcing convexity numbers of graphs resulting from some binary operations

Abstract

Given a connected graph G and two vertices u and v in V (G), I G [u, v] denotes the closed interval consisting of u, v and all vertices lying onevery pair of vertices u, v ∈ C. A subset T of a maximum convex set Sergio R. Canoy Jr. et al.S of G is called a forcing subset for S if S is the unique maximum convex set containing T . The forcing convexity number f con(S) of a maximum convex set S, is the minimum cardinality of a forcing subset for S. The forcing convexity number f con(G) of G is the smallest f con(S) among all maximum convex sets S of G. In this paper, we characterize the forcing subsets in the join and composition of graphs and determine their forcing convexity numbers. Mathematics Subject Classification: 05C69