AVD Total Coloring of Central Graphs, Subdivision Graphs, and the Join of Graphs

Amitayu Banerjee

AVD Total Coloring of Central Graphs, Subdivision Graphs, and the Join of Graphs

Combinatorics 2026-07-02 v1

Authors: Amitayu Banerjee

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 and establish new results on the AVD-total coloring of joins of graphs.

Keywords

AVD total coloring central graphs subdivision graphs join of graphs regular graphs complete bipartite graphs

Cite

@article{arxiv.2607.01979,
  title  = {AVD Total Coloring of Central Graphs, Subdivision Graphs, and the Join of Graphs},
  author = {Amitayu Banerjee},
  journal= {arXiv preprint arXiv:2607.01979},
  year   = {2026}
}

Comments

Presented the main results of this paper in ICGTA-2026 (International Conference on Graph Theory and its Applications-2026)