{
  "abstract": "The adjacent vertex distinguishing (AVD)-total chromatic number $χ''_{a}(G)$ of a graph $G$ is the least integer $k$ for which $G$ has a proper total coloring $f$ with $k$ colors such that $C_G(u)\\neq C_G(v)$ for every edge $uv\\in E(G)$, where $C_G(u)=\\{f(u)\\}\\cup\\{f(uw):uw\\in E(G)\\}$. The AVD-total coloring conjecture (AVD-TCC) asserts that $χ''_{a}(G)\\leq Δ(G)+3$ for every simple graph $G$, where $Δ(G)$ is the maximum degree of $G$. In this paper, we prove the AVD-TCC for certain classes of graph products, including Cartesian products, lexicographic products, skew products, cover products, comb products, and Indu--Bala products.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03411",
  "author_total": 3,
  "authors": [
    {
      "name": "Amitayu Banerjee"
    },
    {
      "name": "Jayabalan Geetha"
    },
    {
      "name": "Kanagasabapathi Somasundaram"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ht2k84m7xyxf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03411",
  "fulltext_url": null,
  "id": "5ht2k84m7xyxf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03411",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Graph Labeling and Dimension Problems"
    ]
  ],
  "openalex": "W7208789443",
  "pdf_url": "https://arxiv.org/pdf/2609.03411",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ht2k84m7xyxf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03411",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03411"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Adjacent vertex distinguishing total chromatic number of graph products",
  "title_text": "Adjacent vertex distinguishing total chromatic number of graph products",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/5ht2k84m7xyxf",
  "venue": "arXiv",
  "versions": []
}