On Cliques and Forcing \(m\)-Convexity Numbers of Graphs

Abstract

This paper introduces the concepts of forcing \(m\)-convexity number and forcing clique number of a graph. We show that the forcing \(m\)-convexity numbers of some Cartesian product and composition of graphs are related to the forcing clique numbers of the graphs. We also show that the forcing \(m\)-convexity number of the composition \(G[K_n]\), where \(G\) is a connected graph with no extreme vertex, is equal to the forcing \(m\)-convexity number of \(G\).