A labeling approach to vertex N-magic weighted total graphs with vertex-odd values

Abstract

The current text discusses the concept of odd vertex N-magic total graphs, a novel idea in the realm of vertex N-magic-type graphs. This idea is defined by N- magic with distinct degrees and identifies odd vertex labels relevant to this property. This manuscript offers a novel approach to labeling graphs, focusing on a specific type of graph. It outlines a method for creating labeling functions that meet specific requirements for vertex weights and magic constants. This study explores the practical application of vertex N-magic labeling for modeling employee skills and extracurricular activity networks, where a graph-based approach is employed to examine the relationships and capabilities of employees within replicated corporate settings. Graph theory’s versatility is demonstrated through its application in both theoretical research and real-world data analysis, highlighting the effectiveness of vertex N-magic total labeling. It concludes with an examination of a specific approach for utilizing the proposed labeling along with an unresolved issue.