The rainbow connection number of graph resulting for operation of sun graph and path graph

Abstract

Let G is a connected graph. A rainbow k-coloring on G is a function c: E(G) → {1, ⋯, k} for k ϵ ℕ where for any two vertices u and v in V, there is a path which all edges have no same color. A path that all edges have no the same color is called a rainbow path. Let k is the smallest positive integer that is needed to make G be rainbow connected, then k is called by the rainbow connection number of G symbolized by rc(G). There are many researches on rainbow connection number of operation graph classes that have been done. In this paper, we use join product and strong product as operations on sun graph cn⊙k̄1 and path graph Pm for determining the rainbow connection number.