Certain Results on Prime and Prime Distance Labeling of Graphs

The necessity for good and tenable communication systems has motivated researchers to develop mobile communication networks (MCN). On the other hand, the huge functionalities of the global system of mobile (GSM) communication have given an increasing number of users. As the subscribers grow, the necessity for efficient and productive planning of the limited frequency spectrum of the GSM is inevitable, especially in highly dense areas. Researchers have proposed various algorithms for frequency or channel allocation (CA), as the discussions about CA methods to resolve the various practical issues in CA are going on. The literature reveals that the “Manhattan distance” concept can be used in scheduling and optimization problems. Similarly, the same idea makes it possible to discover a more tenable telecommunication system with “ease of connectivity” among subscribers, even when many users are on a common channel. Graph labeling is the most interesting idea in graph theory that has numerous uses in different fields, particularly in communication networks. 2-odd labeling assigns distinct integers to the nodes of a graph $$G\left( {V,E} \right)$$ such that the positive difference of adjacent nodes is either 2 or an odd integer, $$2k \pm 1,\;k \in N$$ . The motivation behind the development of this article is to study the applications of graph theory in communication networks through the concept of 2-odd labeling in graphs. 

Studying the Applications of Graph Labeling in Satellite Communication Through 2-Odd Labeling of Graphs

A graph G is a prime distance graph if its vertices can be labeled with distinct integers in such a way that for any two adjacent vertices, the absolute difference of their labels is a prime number. It is known that cycles and bipartite graphs are prime distance graphs. In this paper we derive certain general results concerning prime distance labeling. We also investigate prime distance labeling of some cycle related graphs in the context of some graph operations, namely, power, fusion, duplication and vertex switching in cycle $C_n$.

A. Parthiban

Papers

On Prime Distance Labeling of Graphs