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

Lyra Yulianti, Muhardiansyah Muhardiansyah, Admi Nazra

Abstract


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.

Keywords


rainbow connection number; wheel; line graph; middle graph; total graph

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DOI: http://dx.doi.org/10.5614/ejgta.2025.13.1.2

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