Radio Labelings of Lexicographic Product of Some Graphs

Labeling of graphs has defined many variations in the literature, e.g., graceful, harmonious, and radio labeling. Secrecy of data in data sciences and in information technology is very necessary as well as the accuracy of data transmission and different channel assignments is maintained. It enhances the graph terminologies for the computer programs. In this paper, we will discuss multidistance radio labeling used for channel assignment problems over wireless communication. A radio labeling is a one-to-one mapping ℘:VG⟶ℤ+ satisfying the condition |℘μ−℘μ′|≥diamG+1−dμ,μ′:μ,μ′∈VG for any pair of vertices μ,μ′ in G. The span of labeling ℘ is the largest number that ℘ assigns to a vertex of a graph. Radio number of G, denoted by rnG, is the minimum span taken over all radio labelings of G. In this article, we will find relations for radio number and radio mean number of a lexicographic product for certain families of graphs.