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 ) + | f ( u ) – f ( v ) | ≥ 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 s p ( f ) = max { | f ( u ) – f ( v ) | : u , v ∈ 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.