On the rainbow connection numbers of line, middle, and total graphs of wheels - Yulianti, Lyra; Muhardiansyah, Muhardiansyah; Nazra, Admi (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2025)
An edge-colored graph G is called rainbow connected if any two vertices in G are connected by a path whose no two edges are colored the same. The rainbow connection of G, denoted by rc(G), is the smallest number of colors needed such that G be a rainbow connected graph. Similarly defined, an edge-colored graph G is called strong rainbow connected if any two vertices in G are connected by a geodesic path whose no two of its edges are colored the same. The strong rainbow connection for G, denoted by src(G), is the smallest number of colors needed such that G be a strong rainbow connected graph. This paper considers the determination of the rainbow connection and strong rainbow connection numbers of the line graph, the middle graph, and the total graph of a wheel Wn on n + 1 vertices.