The Total Difference Chromatic Number of the Book Graphs Bn and K1,1,n

Abstract

A graph G is a discrete structure in Mathematics consisting of points (vertices) and line segments (edges) joining these points. The subject pertaining to the study of graphs is called Graph Theory. Rosa (1967) introduced a graph labeling technique called β-valuation, which was subsequently renamed graceful labeling by Goloumb (1972). Later many real-life practical problems and situations prompted the introduction and study of various labeling techniques like prime labeling, cordial and mean cordial labeling, magic, antimagic and zero-edge magic labeling, friendly labeling, lucky labeling etc., by many authors and researchers. Ranjan Rohatgi and Yufei Zang (2020) introduced the concept of total difference labeling of graphs. A general book graph may be considered to be a graph formed by multiple cycles sharing a common edge. This paper discusses the total difference labeling technique for two classes of the Book graphs, namely the quadrilateral book B_n and the triangular book K_1,1,n.