Radial Radio Number of Hexagonal and Its Derived Networks

Abstract

A mapping ℸ : V G ⟶ N ∪ 0 for a connected graph G = V , E is called a radial radio labelling if it satisfies the inequality ℸ x − ℸ y + d x , y ≥ rad G + 1 ∀ x , y ∈ V G , where rad G is the radius of the graph G . The radial radio number of ℸ denoted by r r ℸ is the maximum number mapped under ℸ . The radial radio number of G denoted by r r G is equal to min { r r ℸ / ℸ is a radial radio labelling of G }.