On d-local strong rainbow connection number of prism graphs

A u − v rainbow path is a path that connects two vertices u and v in a graph G and every edge in that path has a different color. A connected graph G is called a rainbow graph if there is a rainbow path for every pair of vertices in G. For any two vertices u and v in G, a rainbow u − v geodesic in G is the shortest rainbow u − v path. The d-local strong rainbow number (lsrcd) is the smallest number of colors needed to color the edges of G such that any two vertices with distance at most d can be connected by a rainbow geodesic. Thus, the value of d is in the interval 1 < d < diam(G). In this paper, we show the lsrcd of prism graphs with d = 2 and d = 3, and the generalized formula of lsrcd for any value of d.