2-ODD LABELING OF GRAPHS USING SOME GRAPH OPERATIONS

2-ODD LABELING OF GRAPHS USING SOME GRAPH OPERATIONS

A. A. Pir, A. Parthiban, K. Singh

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Abstract

2-odd labeling assigns distinct integers to the nodes of a graph G(V;E) in such a manner, that the positive di erence of adjacent nodes is either 2 or an odd integer, 2k  1; k 2 N. So, G is a 2-odd graph if and only if it permits 2-odd labeling. It is interesting and challenging to study certain important modi cations through various graph operations on a given graph. These operations mainly modify the structure of the underlying graph and so having some understanding of the complex operations which can be done over a graph or a set of graphs is inevitable. The motivation behind the development of this article is to apply the concept of 2-odd labeling on graphs generated by using various graph operations, besides recalling a few interesting applications of graph labeling and graph coloring.

Keywords

2-odd labeling, union, intersection, duplication, extension.