Strong Rainbow Connection Number Of Prism Graphs Having Pendant Edges
Moh Ilham Nardiansyah and Purwanto

Mathematics Department, Malang State of University, Semarang Street 5, Malang, East Java, 65145, Indonesia

Abstract

Abstract. Let G be a finite and simple graph having a vertex set V(G) and an edge set E(G). When u,v \in V(G), the distance of u and v is denoted by d(u,v). A rainbow u-v geodesic in G is an u-v paths of length d(u,v) and all its edges are colored by different colors. If there exist a rainbow u-v geodesic for every pair of distinct vertices u,v \in V(G), then G is called strongly rainbow connected graph. The smallest number of colors needed to make G strongly rainbow connected is strong rainbow connection number of G, Its admits by src(G). A prism C_{m}xP_{2} is the cartesian product of a cycle C_{m} and a path P_{2}. A prism graph having t pendant edges. denoted by [C_{m}xP_{2}]^{t}, is a graph obtained by attaching at least one pendant to each vertex of in the prism. In this paper we study the strong rainbow connection number of [C_{m}xP_{2}]^{t}

Keywords: Strong rainbow connection - prism - pendant

Topic: Mathematics