2-ODD labeling of graphs using some graph operations

Abstract

2-odd labeling assigns distinct integers to the nodes of a graph G(V, E) in such a manner, that the positive difference of adjacent nodes is either 2 or an odd integer, 2k ± 1, k ? 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 modifications 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.