Further results on the radio number of trees

Abstract

Let $G$ be a finite, connected, undirected graph with diameter $diam(G)$ and $d(u,v)$ denote the distance between $u$ and $v$ in $G$. A radio labeling of a graph $G$ is a mapping $f:V(G)\to \{0,1,2,...\}$ such that $|f(u)-f(v)|\ge diam(G)+1-d(u,v)$ for every pair of distinct vertices $u,v$ of $G$. The radio number of $G$, denoted by $rn(G)$, is the smallest integer $k$ such that $G$ has a radio labeling $f$ with $\max \{f(v):v\in V(G)\}=k$. In this paper, we determine the radio number for three families of trees obtained by taking graph operation on a given tree or a family of trees.

7 Pages, CTGTC 2016 conference proceedings paper