Investigating Distance Magic Labeling In Mycielskian Graphs: Properties And Patterns

Abstract

Distance magic labeling is a fascinating topic within graph theory that assigns distinct integers to the vertices of a graph such that the sum of labels of all vertices at a fixed distance from a given vertex is constant. This paper investigates the application of distance magic labeling to Mycielskian graphs, a class of graphs constructed to increase chromatic number without introducing additional cliques. The study delves into the unique properties of Mycielskian graphs and explores the existence and conditions under which they exhibit distance magic labeling. Through theoretical analysis and pattern recognition, we identify key characteristics of Mycielskian graphs that make them suitable for distance magic labeling. Furthermore, we discuss algorithmic approaches for efficiently determining such labelings and present illustrative examples to highlight critical results. The findings contribute to a deeper understanding of labeling in Mycielskian graph structures and open new avenues for further research in graph labeling theories and applications.