Desi Rahmadani, Ghifary Ramadhana Fauziah, Toto Nusantara, Makbul Muksar
An edge-coloring of a graph G is called a rainbow if any two vertices are connected by a path of edges of different colors. The strong rainbow connection number is an extension of the rainbow connection numbers, where it refers to the shortest path, commonly known as the geodesic path. If G is a connected graph and every pair of vertices in G has a geodesic path whose edges do not have the same color, then G is strongly rainbow-connected. The rainbow and strong rainbow connection numbers of a graph G, denoted by rc(G) and src(G), respectively, are the minimum number of colors that are needed to make G rainbow and strongly rainbow connected. This study is interesting, and recently, quite a lot of papers have been published about it. Some previous results only gave the lower and upper bound of rc(G) and src(G). Thus, finding an exact value of rc(G) and src(G) is significantly challenging. In this paper, we determine the exact values of rainbow and strong rainbow connection numbers on pleated of the Dutch windmill graphs. © 2024 American Institute of Physics Inc.. All rights reserved.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Malang, Malang, Indonesia
