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 -