MAXIMUM NONTRIVIAL CONVEX COVER NUMBER OF JOIN AND CORONA OF GRAPHS

Abstract

Let G be a connected graph. We say that a set S ⊆ X(G) is convex in G if, for any two vertices x, y ∈ S, all vertices of every shortest path between x and y are in S. If 3 ≤ |S| ≤ |X(G)| − 1, then S is a nontrivial set. The greatest p ≥ 2 for which there is a cover of G by p nontrivial and convex sets is the maximum nontrivial convex cover number of G. In this paper, we determine the maximum nontrivial convex cover number of join and corona of graphs.