On the Radio Antipodal Mean Number of Some Grid Related Graphs
T. Arputha Jose, R. Prabakaran, R. Gomathy · 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 \(d(u,v) < \textrm{diam}(G)\) and \(d(u,v)+ \Big\lceil \frac{f(u)+f(v)}{2} \Big\rceil \geq \textrm{diam}(G)\), where \(d(u,v)\) represents the shortest distance between any pair of vertices \(u\) and \(v\) of \(G\) and \(\textrm{diam}(G)\) denotes the diameter of \(G\). The radio antipodal mean number of \(f\), denoted by \(r_{\textit{amn}}(f)\) is the maximum number assigned to any vertex of \(G\). The radio antipodal mean number of \(G\), denoted by \(r_{\textit{amn}}(G)\) is the minimum value of \(r_{\textit{amn}}(f)\) 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.