Some Results on Odd-Even Congruence Labeling of Graphs

Introduction: Labeling of graphs has been introduced in 1966. Assignment of natural numbers to vertices and/or edges is referred as graph labeling. Inspired by the ample application of graph labeling technique in real life problems, multifarious labeling strategy was adopted and investigated by many researchers. Objectives:Graph labeling plays a vital role in various fields and can be implemented in multitudinous discipline including coding theory, X-ray, Psychology, crystallography, circuit design, communication networks, astronomy, radar, data security, secret sharing, data base management and so on. Apart from these labeling techniques serve as a model to understand discrete mathematical domains. Methodology:In this paper, an attempt has been made to introduce new labeling such as odd-even congruence labeling. Congruence Graph Labeling is an allocation of natural numbers as labels for the edges and vertices of a graph based on modular arithmetic property. Odd-even congruence labeling is an allocation of odd integers to vertices and even integers to edges in addition to congruence graph labeling. Result: The suggested labeling has been identified on complete bipartite graph, comb graph and spliting graph of a star graph. Further, it is proved that graph acquired by connecting two copies of even cycle Cr by a path Pt, K1,t⊗P2 and D2 (Pt) are odd-even congurence graph.