Abstract
A u − ν rainbow path is a path that connects two vertices u and ν 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 ν in G, a rainbow u − ν geodesic in G is the shortest rainbow u − ν path. The d-local strong rainbow number (lsrc d ) 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 lsrc d of prism graphs with d = 2 and d = 3, and the generalized formula of lsrc d for any value of d.
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