Local strong rainbow connection number of corona product between cycle graphs

Abstract

A rainbow geodesic is a shortest path between two vertices where all edges are colored differently. An edge coloring in which any pair of vertices with distance up to d, where d is a positive integer that can be connected by a rainbow geodesic is called d-local strong rainbow coloring. The d-local strong rainbow connection number, denoted by lsrc_d(G), is the least number of colors used in d-local strong rainbow coloring. Suppose that G and H are graphs of order m and n, respectively. The corona product of G and H, G ⊙ H, is defined as a graph obtained by taking a copy of G and m copies of H, then connecting every vertex in the i-th copy of H to the i-th vertex of G. In this paper, we will determine the lsrc_d(C_m ⊙ C_n) for d=2 and d=3.