Local strong rainbow connection number of corona product between cycle graphs

Khairunnisa N. Afifah (Universitas Indonesia)
Kiki A. Sugeng (Universitas Indonesia)

Indonesian Journal of Combinatorics
Vol 7, No 1 (2023)

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 lsrcd(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 lsrcd(Cm ⊙ Cn) for d=2 and d=3.