Rainbow connection number of Cm o Pn and Cm o Cn
Abstract
Let G = (V(G),E(G)) be a nontrivial connected graph. A rainbow path is a path which is each edge colored with different color. A rainbow coloring is a coloring which any two vertices should be joined by at least one rainbow path. For two different vertices, u,v in G, a geodesic path of u-v is the shortest rainbow path of u-v. A strong rainbow coloring is a coloring which any two vertices joined by at least one rainbow geodesic. A rainbow connection number of a graph, denoted by rc(G), is the smallest number of color required for graph G to be said as rainbow connected. The strong rainbow color number, denoted by src(G), is the least number of color which is needed to color every geodesic path in the graph G to be rainbow. In this paper, we will determine the rainbow connection and strong rainbow connection for Corona Graph Cm o Pn, and Cm o Cn.
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PDFDOI: http://dx.doi.org/10.19184/ijc.2019.3.2.3
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