On the rainbow connection numbers of line, middle, and total graphs of wheels

Yulianti, Lyra (Department of Mathematics and Data Science, Faculty of Mathematics and Natural Sciences, Universitas Andalas)
Muhardiansyah, Muhardiansyah (Department of Mathematics and Data Science, Faculty of Mathematics and Natural Sciences, Universitas Andalas)
Nazra, Admi (Department of Mathematics and Data Science, Faculty of Mathematics and Natural Sciences, Universitas Andalas)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 13, No 1 (2025): Electronic Journal of Graph Theory and Applications

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.