Radio Number of 1, 2 - Cartesian Product of Paths

By : D. Rambabu, P. Venkata Subba Reddy,

Page No: 31-38

Abstract
Let G be a simple, connected and undirected graph. A radio labeling f of G is an assignment of positive integers, called labels to the vertices of G such that if u, v ? V (G) are distinct then ?f(u) ? f(v)? ? D(G) + 1 ? d (u, v), where D(G) is the diameter of the graph G and d (u, v) is the distance between the vertices u and v in G. The maximum label (positive integer) assigned by f to some vertex of G is called the span of f. The radio number of G denoted by rn(G) is the minimum span over all radio labelings of G. In this paper, we prove a lower bound for the 1 , 2 -Cartesian product of paths.

Authors :
Raaghave Sood, P. Venkata Subba Reddy and D. Rambabu : Department of Computer Science and Engineering National Institute of Technology Warangal - 506 004, India.