Some new odd-even congruence graphs

Abstract

Introduction: The concept of labeling of graph has been introduced in mid-1960. A graph labeling is an assignment of integers to the nodes or edges or both depends on specific conditions. Many types of graph labeling techniques have been studied by several authors. 

Objectives: Labeling of graphs has remarkable applications in diverse fields like the study of the physical cosmology, debug circuit design, X-ray, crystallography, astronomy, radar, broadcasting network, secret sharing, database management, coding theory and much more. Besides these graph labeling techniques analyze and solve various graph related problems.

Methods: This research paper focuses on Odd-even congruence labeling of different types of graphs. Assignment of natural numbers as labels for the edges and vertices of a graph based on modular arithmetic property known as congruence graph labeling.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 triangular snake graph, ladder graph, coconut tree, triangular book, friendship graph.