Radio number for middle graph of paths

Abstract

For a connected graph $G$, let $diam(G)$ and $d(u,v)$ denote the diameter of $G$ and distance between $u$ and $v$ in $G$. A radio labeling of a graph $G$ is a mapping $\phi :V(G)\to \{0,1,2,...\}$ such that $|\phi (u)-\phi (v)|\ge diam(G)+1-d(u,v)$ for every pair of distinct vertices $u,v$ of $G$. The span of $\phi$ is defined as span($\phi$) = $\max \{|\phi (u)-\phi (v)|:u,v\in V(G)\}$. The radio number $rn(G)$ of $G$ is defined as $rn(G)$ = $\min \{$span($\phi$) : $\phi$ is a radio labeling of $G\}$. In this paper, we determine the radio number for middle graph of paths.

8 Pages, CTGTC 2016 conference proceedings paper