AI 中文总结
本文验证了正则图、完全二部图等中心图满足AVD全染色猜想，并确定了细分图的AVD全色数，给出了图并的AVD全染色新结果。
AI 中文摘要
2020年，Panda、Verma和Keerti提出：是否每个图的中心图都满足AVD全染色猜想？本文验证了正则图、完全二部图、可表示为两个同阶图并的图以及其他若干图类的中心图满足该猜想，从而为该开放问题提供了部分进展。我们进一步确定了细分图的AVD全色数，并建立了关于图并的AVD全染色的新结果。
英文摘要
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.
CommentsPresented 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
