Radial Radio Number of Hexagonal and Its Derived Networks

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 }.

Zagreb Radio Indices and Coindices

Zagreb radio index or coindex of a graph is defined based on the optimal radio labelling of the graph, where optimal refers to the labeling with a span equal to the radio number of the graph. We have defined the first and second Zagreb radio coindex, third Zagreb radio index, and coindex and calculated its value for some famous graphs. Furthermore, we established a certain relationship between Zagreb radio indices and the coindices of graphs.