Abstract
A graph labeling problem is an assignment of labels to the vertices or edges (or both) of a graph G satisfying some mathematical condition. Radio Mean Labeling, a vertex-labeling of graphs with non-negative integers has a significant application in the study of problems related to radio channel assignment. The maximum label used in a radio mean labeling is called its span, and the lowest possible span of a radio mean labeling is called the radio mean number of a graph. In this paper, we obtain the radio mean number of paths and total graph of paths.
Highlights
For basic graph theory terminology, we refer [16]
The channel assignment problem is to assign radio channels to transmitters with minimum span in such a way that it minimizes interference between radio stations that are in the same neighborhood
This problem of Radio channel assignment can be converted into a Graph theoretic problem as follows: The radio network can be considered as a graph in which vertices corresponds to transmitter locations and two vertices are adjacent if the locations of the radio stations corresponding to these vertices are close
Summary
For basic graph theory terminology, we refer [16]. The basic principle of a Radio communication network is transmission and reception of radio signals. The radio mean number of f or rmn(f) is the maximum integer assigned to any v∈ V(G) under this mapping f.
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