On the Locating Rainbow Connection Number of the Comb Product with Complete Graphs or Trees

This paper investigates the locating rainbow connection number ( \({ \text {rvcl}}(G)\) ) of comb products of graphs. We introduce the concept of a rainbow-vertex \(\ell \) -coloring and define the locating rainbow connection number within this framework. Our main results establish tight upper and lower bounds for \({ \text {rvcl}}(G)\) in the context of comb products. Additionally, we determine the locating rainbow connection number for the comb product of an arbitrary graph with a complete graph or a tree.