Radio Labeling for Strong Product K₃ ⊠ P_n

Abstract

Many variations of graph labeling has been defined in the literature. e.g., graceful, harmonious and radio labeling etc. In information technology and in data sciences, we need secrecy of data, different channel assignment and accuracy of transmission of the data. This make the use of graph terminologies indispensable for the computer programs. In this paper, we will discuss multi-distance radio labeling used for channel assignment problem over a wireless communication. A radio (multi-distance) labeling of a graph G is a function h from V(G) to the set of non-negative integers such that |h(u) - h(v)| ≥ diam(G) + 1 - dG(u, v), Where diam(G) and dG(u, v) are diameter and distance between u and v in graph G respectively. The span of a radio labeling h is the maximum integer assigned by h and radio number of a graph G is the minimum span taken over all radio labeling of G. In this article, we will find relations for radio number of a strong product K3 ⊗ Pn, n ≥ 3.

Keywords

• Channel assignment
• radio labeling
• radio number
• strong product
• complete graph
• path