On radio coloring of Bistar graph families

Radio k - Coloring of graph G is one of the divergence of frequency assignment problem (FAP). A simply connected graph G with diam(G) and a positive integer k, 1 ≤ k ≤ diam(G), a radio k - coloring of G is an allocation φ of positive integers to the nodes of G such that ϕ(u)−ϕ(v)≥1+k−d(u,v), where u and v are any two different nodes of G and d(u, v) is the interval betwixt u and v. The supreme color granted by φ is called span, denoted by rck (φ). The radio k - chromatic number rck (G) of G is the minimal {rck (φ) : φ is a radio k - coloring of G}. In this paper,we attain the exact value of the radio k - chromatic number of bistar graph Bn,m and an operations on middle graph, central graph, total graph, line graph and jump graph of bistar graph denoted by M(Bn,m),C(Bn,m), T (Bn,m), L(Bn,m) and J(Bn,m) respectively.