The (strong) rainbow connection number of stellar graphs
Ahmad Shulhany, A.N.M. Salman · AIP conference proceedings · 2016
Let G = (V,E) be a simple, connected, and finite graph.A function c from E to {1, 2, ..., k} is said rainbow kcoloring of G, if for any pair of vertices u and v in V, there exists au -vpath whose edges have different colors.The rainbow connection number of G, denoted by rc(G), is the smallest positive integer k such that Ghas a rainbow kcoloring.Furthermore, such the function c is said strong rainbow k-coloring, if for any pair of vertices u and v in V, there exists a rainbow u-v path with its length is equal to distance betweenu and v.The smallest positive integer k such that G has a strong rainbow k-coloring is defined as the strong rainbow connection number, denoted by src(G).In this paper, we introduce a new class of graphs, namely stellar graphs.A stellar graph on 2mn+1 vertices, denoted by , is the corona product of a trivial graph and mcopies ladder graph on 2n vertices (K 1 m. ).We determine the (strong) rainbow connection number of stellar graphs.