Star-rainbow coloring in some corona product graphs

Abstract

Abstract A “rainbow connected graph” is a connected graph in which every pair of distinct vertices in it has a rainbow path, in the sense that no two edges in this path are colored the same. The rainbow connection number of a connected graph G, denoted by rc(G), is the “minimum” number colors necessary to color G such that it has a rainbow path between every pair of its vertices. Further, G is said to be star-rainbow colored if every path on four vertices in it is rainbow colored. The “minimum” number of colors that are necessary to color G such that it is star-rainbow colored is called the “star-rainbow connection number” of G, denoted by strrc(G). In this article, we consider some corona product graphs involving Pn , Kn , Cn and K 1,n and find strrc(G) for such graphs.