On Radio -Chromatic Numbers for the Family of Triple Star Graphs

Let G=(G), E(G)\ be a simple connected graph with diameter $d(G)$ and k be a positive integer. A radio k-coloring of a graph is a proper node coloring that is an assignment f of positive integers to the nodes of G such that |f(x)-f(y)| ≥ k+1-d(x, y), where x and y are two distinct nodes, and $d(x, y)$ is the length between x and y. The maximum color assigned to some node of $f(V(G))$ is called the span of f and it is indicated by span(f). The least span over all radio k-coloring of G is the radio k-chromatic number of G and it is indicated by r c_(G). In this paper, we investigate the radio k-chromatic number for the triple star graph K1, n, n, n and its middle graph M(K1, n, n, n), central graph C(K1, n, n, n), total graph T(K1, n, n, n) and line graph L(K1, n, n, n).