Radial radio number of chess board graph and king’s graph

Abstract

A radial radio labeling ℸ of a connected graph G = (V, E) with radius rad(G) is a mapping from V (G) to N ∪ {0} satisfying |ℸ(u) − ℸ(w)|+ d(u, w) ≥ 1 + rad(G), ∀ u, v ∈ V (G). The span of a radial radio labeling ℸ, denoted by rr(ℸ) is the greatest number in the range of ℸ. The minimum span taken over all radial radio labelings ℸ of G is called the radial radio nmber of G and it is denoted by rr(G). In this article, we have investigated the upper bounds for rr(G) of chess board graphs and king’s graph.