On the Radio Antipodal Mean Number of Some Grid Related Graphs - Jose, T. Arputha; Prabakaran, R.; Gomathy, R. (Communications in Mathematics and Applications, 2023)
The radio antipodal mean labeling of a graph \(G\) is a function \(f\) that assigns to each vertex \(u\), a non-negative integer \(f(u)\) such that \(f(u) eq f(v)\) if \(d(u,v) < diam(G)\) and \(d(u,v)+ \Big\lceil \frac{f(u)+f(v)}{2} \Big\rceil ≥ diam(G)\), where \(d(u,v)\) represents the shortest distance between any pair of vertices \(u\) and \(v\) of \(G\) and \(diam(G)\) denotes the diameter of \(G\). The radio antipodal mean number of \(f\), denoted by \(r_{amn}(f)\) is the maximum number assigned to any vertex of \(G\). The radio antipodal mean number of \(G\), denoted by \(r_{amn}(G)\) is the minimum value of \(r_{amn}(f)\) taken over all antipodal mean labeling \(f\) of \(G\). In this paper, the exact values of radio antipodal mean number of some grid related graphs have been obtained.
Keywords: Communication networks; Channel assignment problem; Radio labeling; Radio antipodal mean number; Triangular grid; Torus grid