V2I12P17

Odd-Even Congruence Labelling of Some Well-Known Graphs

Rituraj^1*, Shambhu Kumar Mishra²

Abstract

Introduction: In the field of graph theory, graph labelling is one of the fastest growing area. A graph labeling is defined as an assignment of integers to the nodes or edges or both based on certain conditions. Many types of graph labeling techniques have been studied by several authors.

Objectives: The application of labelling of graphs has  diverse fields in the study of the data base management, secret sharing schemes, physical cosmology, debug circuit,  X-ray, crystallography, astronomy, radar and much more.

Methods: This paper is based on Odd-even congruence labeling of different types of graphs. The vertices and edges are labeled by an assignment of natural numbers. It is based on  modular arithmetic property known as congruence graph labelling of a graph. In congruence graph labelling vertices are assigned by odd integers and edges are assigned by even integers with the property of congruence labelling.

Results: This labeling method has been identified on tadpole graph, pan graph, generalized Petersen graph, wheel graph.

Keywords:

Labeling, Congruence labeling, Odd-even congruence labeling