Radio Antipodal Labeling of Mongolian Tent and Torus Grid Graphs

Abstract

An antipodal labeling is a function \(f\ \)from the vertices of \(G\) to the set of natural numbers such that it satisfies the condition \(d(u,v) + \left| f(u) - f(v) \right| \geq d\), where d is the diameter of \(G\ \)and \(d(u,v)\) is the shortest distance between every pair of distinct vertices \(u\) and \(v\) of \(G.\) The span of an antipodal labeling \(f\ \)is \(sp(f) = \max\{|f(u) - \ f\ (v)|:u,\ v\, \in \, V(G)\}.\) The antipodal number of~G, denoted by~an(G), is the minimum span of all antipodal labeling of~G. In this paper, we determine the antipodal number of Mongolian tent and Torus grid.