Certain Topics Pertaining to Graph Labeling

Abstract

Methods: Different approaches and methodology were applied depending upon the challenges and requirements posed in Graph Labeling. The application of essential and conceptual methodology formed very foundation of the structure. Here is an outline of the research work. newline A probe into Various Graph Labeling Techniques; newline Introduction of New Graph Labeling Techniques and Innovative Results; newline Find New Families of Graphs in Cordial Labeling; newline Find New Families of Graphs in k-equitable Labeling; newline Find New Families of Graphs in k-cordial Labeling; newlineIn the course of Research work the Researcher has referred reference books and research papers published in reputed National/International journals which related to research area. An in depth study of reputed e-journals to review the research papers in the field of Graph Labeling Techniques have also been conducted to lend a depth and perspective. newlineResults and Discussion: This research work deals with the k-cordial labeling and the content is presented in six chapters. The First Chapter is of introductory nature while the Second Chapter serves as background for the subsequent chapters. The Third Chapter is focused on 5-cordial labeling of graphs, reporting some of the existing results and contributing fourteen new results. The Fourth Chapter is targeted to discuss 7-cordial labeling of graphs and contributes nine new results to the theory of 7-cordial graphs. The investigation of k-cordial labeling for some standard graphs has been done in Fifth Chapter. The last Chapter is focused on the discussion on k-cordial labeling of path and cycle in the context of vertex switching. newlineConclusions: In this research work newlinei) Fourteen new results have been derived for 5-cordial labeling. ii) Nine new results have been found for 7-cordial labeling. iii) Fifteen new results have been added in the field of k-cordial labeling. newline