Radio Number for Strong Product $P_{2} \boxtimes P_{n}$

S. K. Vaidyaa,* and D. D. Bantvab

Radio Number for Strong Product $P_{2} \boxtimes P_{n}$

Authors :

S. K. Vaidya^a,* and D. D. Bantva^b

Author Address :

^aDepartment of Mathematics, Saurashtra University, Rajkot-360 005, Gujarat, India.
^bDepartment of Mathematics, L. E. College, Morvi-363 642, Gujarat, India.

*Corresponding author.

Abstract :

A radio labeling of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of non-negative integers such that $|f(u)-f(v)|\geq diam(G) + 1 - d_{G}(u,v)$, where $diam(G)$ and $d_{G}(u,v)$ are diameter and distance between $u$ and $v$ in graph $G$ respectively. The radio number $rn(G)$ of $G$ is the smallest number $k$ such that $G$ has radio labeling with max$\{f(v):v \in V(G)\}=k$. We investigate radio number for strong product of $P_{2}$ and $P_{n}$.

Keywords :

Interference, channel assignment, radio labeling, radio number, strong product.

DOI :

Article Info :

Received : February 22, 2013; Accepted : March 17, 2013.