On the radio antipodal geometric mean number of ladder related graphs

Abstract

Let G(V, E) be a graph with vertex set V and edge set E. A radio geometric mean labeling of a connected graph G is a one to one map from the vertex set V (G) to the set of natural numbers N such that for two distinct vertices u and v, where d(u, v) represents the shortest distance between the vertices u and v and diam(G) represents the diameter of G . Based on the concept of radio geometric mean labeling, a new graph labeling called radio antipodal geometric mean labeling is being introduced in this paper. A radio antipodal geometric mean labeling of a graph G is a mapping from the vertex set V (G) to the set of natural numbers N such that for two distinct vertices u and, then the vertices u and v can be given the same label and if d(u, v) = diam(G) then the vertices u and v should be assigned different labels. The radio antipodal geometric mean number of f , ragmn(f ) is the maximum number assigned to any vertex of G. The radio antipodal geometric mean number of G, ragmn(G) is the minimum value taken over all radio antipodal geometric mean labeling f of G. In this paper, the radio antipodal geometric mean number of certain ladder related graphs have been investigated.

On the Radio Antipodal Mean Number of Some Grid Related Graphs

“…The main reason behind is that it has a wide range of applications in various fields. To list a few, graph labeling is useful in coding theory, astronomy, circuit design,communication network addressing, secret sharing (Giridaran et al [6]).…”