AVD Total Colorings of Subdivision Graphs, Joins, and Deleted Lexicographic Products

Abstract

In 2020, Panda, Verma, and Keerti asked whether the central graph of every graph satisfies the AVD-total coloring conjecture. In this paper, we verify the conjecture for central graphs of regular graphs, complete bipartite graphs, graphs that can be expressed as the join of two graphs of the same order, and several other graph classes, thereby providing partial progress towards this open problem. We further determine the AVD-total chromatic number of subdivision graphs of connected graphs and establish new results on the AVD-total coloring of joins of graphs and deleted lexicographic products.

Presented the main results of this paper in ICGTA-2026 (International Conference on Graph Theory and its Applications-2026). This revised version contains some corrections to the earlier versions