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On WL-Rank and WL-Dimension of Some Deza Circulant Graphs. / Bildanov, Ravil; Panshin, Viktor; Ryabov, Grigory.

In: Graphs and Combinatorics, Vol. 37, No. 6, 11.2021, p. 2397-2421.

Research output: Contribution to journal › Article › peer-review

Harvard

Bildanov, R, Panshin, V & Ryabov, G 2021, 'On WL-Rank and WL-Dimension of Some Deza Circulant Graphs', Graphs and Combinatorics, vol. 37, no. 6, pp. 2397-2421. https://doi.org/10.1007/s00373-021-02364-z

APA

Bildanov, R., Panshin, V., & Ryabov, G. (2021). On WL-Rank and WL-Dimension of Some Deza Circulant Graphs. Graphs and Combinatorics, 37(6), 2397-2421. https://doi.org/10.1007/s00373-021-02364-z

Vancouver

Bildanov R, Panshin V, Ryabov G. On WL-Rank and WL-Dimension of Some Deza Circulant Graphs. Graphs and Combinatorics. 2021 Nov;37(6):2397-2421. doi: 10.1007/s00373-021-02364-z

Author

Bildanov, Ravil ; Panshin, Viktor ; Ryabov, Grigory. / On WL-Rank and WL-Dimension of Some Deza Circulant Graphs. In: Graphs and Combinatorics. 2021 ; Vol. 37, No. 6. pp. 2397-2421.

BibTeX

@article{de251df469914dc18e19591331795d65,
title = "On WL-Rank and WL-Dimension of Some Deza Circulant Graphs",
abstract = "The WL-rank of a digraph Γ is defined to be the rank of the coherent configuration of Γ. The WL-dimension of Γ is defined to be the smallest positive integer m for which Γ is identified by the m-dimensional Weisfeiler–Leman algorithm. We classify the Deza circulant graphs of WL-rank 4. In additional, it is proved that each of these graphs has WL-dimension at most 3. Finally, we establish that some families of Deza circulant graphs have WL-rank 5 or 6 and WL-dimension at most 3.",
keywords = "Circulant graphs, Deza graphs, WL-dimension, WL-rank",
author = "Ravil Bildanov and Viktor Panshin and Grigory Ryabov",
note = "Funding Information: The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.",
year = "2021",
month = nov,
doi = "10.1007/s00373-021-02364-z",
language = "English",
volume = "37",
pages = "2397--2421",
journal = "Graphs and Combinatorics",
issn = "0911-0119",
publisher = "Springer Japan",
number = "6",

}

RIS

TY - JOUR

T1 - On WL-Rank and WL-Dimension of Some Deza Circulant Graphs

AU - Bildanov, Ravil

AU - Panshin, Viktor

AU - Ryabov, Grigory

N1 - Funding Information: The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.

PY - 2021/11

Y1 - 2021/11

N2 - The WL-rank of a digraph Γ is defined to be the rank of the coherent configuration of Γ. The WL-dimension of Γ is defined to be the smallest positive integer m for which Γ is identified by the m-dimensional Weisfeiler–Leman algorithm. We classify the Deza circulant graphs of WL-rank 4. In additional, it is proved that each of these graphs has WL-dimension at most 3. Finally, we establish that some families of Deza circulant graphs have WL-rank 5 or 6 and WL-dimension at most 3.

AB - The WL-rank of a digraph Γ is defined to be the rank of the coherent configuration of Γ. The WL-dimension of Γ is defined to be the smallest positive integer m for which Γ is identified by the m-dimensional Weisfeiler–Leman algorithm. We classify the Deza circulant graphs of WL-rank 4. In additional, it is proved that each of these graphs has WL-dimension at most 3. Finally, we establish that some families of Deza circulant graphs have WL-rank 5 or 6 and WL-dimension at most 3.

KW - Circulant graphs

KW - Deza graphs

KW - WL-dimension

KW - WL-rank

UR - http://www.scopus.com/inward/record.url?scp=85119237438&partnerID=8YFLogxK

U2 - 10.1007/s00373-021-02364-z

DO - 10.1007/s00373-021-02364-z

M3 - Article

AN - SCOPUS:85119237438

VL - 37

SP - 2397

EP - 2421

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

IS - 6

ER -

ID: 34678942