Odd-Even Congruence Labeling of Some Graphs

Introduction: Graph labeling is one of the fastest growing areas in the field of graph theory. A graph labeling is basically an assignment of integers to the nodes or edges or both, subject to certain conditions. Different types of graph labeling techniques have been developed by several authors. Objectives: The applications of labeling of graphs has diverse fields in the study of data base management, secret sharing schemes, physical cosmology, debug circuit design, X-ray, crystallography, astronomy, radar, broadcasting network, secret, coding theory and much more. The graph labeling techniques serve as useful mathematical models and solve various graph related problems. Methods: The strength of this research paper is based on Odd-even congruence labeling of different types of graphs. Assignment of natural numbers as labels for the edges and vertices of a graph. It is based on modular arithmetic property known as congruence graph labelling of a graph. For congruence graph labeling it entails the assignment of odd integers to vertices and even integers to edges with property of congruence graph labeling. Results: This labeling method has been identified on friendship graph, shell graph, generalized butterfly graph, fan graph, P₂+mK₁ graph