The Rainbow Connection Number of an n-Crossed Prism Graph and its Corona Product with a Trivial Graph

Let G = (V(G), E(G)) be a simple, finite, and connected graph. Let k be a positive integer. Define an edge k-coloring, c : E(G) →{1, 2, ..., k} where adjacent edges may be colored the same. Let x and y in V(G). An x − y path in G is called a rainbow path, if there are no two edges with the same color in this path. An edge k-coloring c is called rainbow k-coloring, if for any two distinct vertices x and y in V(G), there is an x − y rainbow path. The rainbow connection number, denoted by rc(G), is the smallest positive integer k such that G has a rainbow k-coloring. In this paper, we determine the rainbow connection number of an n-crossed prism graph and its corona product with a trivial graph