RADIO ANTIPODAL MEAN LABELING OF TRIANGULAR SNAKE FAMILIES

T. J. Arputha, P. Venugopal and M. Giridaran

  DOI:  https://doi.org/10.37418/amsj.9.11.82

Full Text

Let $G=(V,E)$ be a graph with vertex set $V$, edge set $E$ and $diam(G)$ be the diameter of $G$. Let $u,v \in V(G)$. The \textit{radio antipodal mean labeling} of graph $G$ is a function $f$ that assigns to each vertex $u$, a non-negative integer $f(u)$ such that $f(u) \neq f(v)$ if $d(u,v)<diam(G)$ and $d(u,v)+\lceil \frac{f(u)+f(v)}{2} \rceil \geq diam(G)$, where $d(u,v)$ represents the shortest distance between any pair of vertices $u$ and $v$ of $G$. The antipodal mean number of $f$, denoted by $r_{amn}(f)$ is the maximum number assigned to any vertex of $G$ and is denoted by $amn(f)$. The 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, we have obtained the upper bounds of radio antipodal mean number of triangular snake families.

Keywords: Radio labeling, triangular snake, alternate triangular snake, double triangular snake, double alternate triangular snake.