The Rainbow Vertex Connection Number of Some Amalgamation of Two Cycles

Abstract

This paper focuses on rainbow vertex coloring in a graph G, in which, for every two vertices in G, there exists a rainbow vertex path where all internal vertices have distinct colors. The rainbow vertex connection number of G, denoted by rvc(G), is the minimum number of colors required to make G rainbow-vertex connected. In this paper, we determine the rainbow vertex connection number of some amalgamation of two cycles.