A Study on the Total Coloring and Equitable Total Coloring for Splitting Graph

This study focuses on the total coloring and equitable total coloring of splitting graphs, an area of graph theory that examines the assignment of colors to both vertices and edges under specific constraints. Total coloring involves assigning distinct colors to adjacent or incident elements (vertices and edges) in such a way that no two adjacent or incident elements share the same color. Equitable total coloring further requires the distribution of colors across vertices and edges to be as balanced as possible. The splitting graph, derived from a base graph by splitting its vertices, presents unique challenges in both total and equitable total coloring. This research explores the chromatic bounds, methods of achieving minimal colorings, and equitable distribution strategies for splitting graphs. The findings contribute to a deeper understanding of coloring properties in modified graph structures, with implications for both theoretical and practical applications.