Relationship between radio k-chromatic number of graphs and square graphs

Abstract

Let be a simple connected graph with diameter d(G) and k be a positive integer. A radio k-labeling of G is a function such that holds for each pair of distinct vertices u and v of G, where is the distance between u and v in G. The absolute difference of the largest and smallest values in is termed as the span of f, and is denoted by The minimum span amongst all radio k-labelings of G is the radio k-chromatic number of G and it is denoted by In this article, we investigate a relationship between the radio k-chromatic number of an arbitrary graph and its square graph. This investigation leads us to the exact value of the radio number for square of graphs with small triameter.

Keywords

• frequency assignment problem
• radio k-labeling
• radio k-number
• square of graphs
• span