On a Family of Divisible Design Digraphs

Mikhail Muzychuk; Grigory Ryabov

doi:10.1007/s00373-025-02941-6

On a Family of Divisible Design Digraphs

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

Abstract

For every odd prime power q, a family of pairwise nonisomorphic normal arc-transitive divisible design Cayley digraphs with isomorphic neighborhood designs over a Heisenberg group of order q3 is constructed. It is proved that these digraphs are not distinguished by the Weisfeiler–Leman algorithm and have the Weisfeiler–Leman dimension 3.

Original language	American English
Article number	75
Journal	Graphs and Combinatorics
Volume	41
Issue number	4
DOIs	https://doi.org/10.1007/s00373-025-02941-6
State	Published - 1 Aug 2025
Externally published	Yes

Keywords

Cayley digraphs
Divisible design digraphs
Weisfeiler–Leman dimension

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Access to Document

10.1007/s00373-025-02941-6

Cite this

@article{5d7e5f0de3f8485bb5e770a290fb42c4,

title = "On a Family of Divisible Design Digraphs",

abstract = "For every odd prime power q, a family of pairwise nonisomorphic normal arc-transitive divisible design Cayley digraphs with isomorphic neighborhood designs over a Heisenberg group of order q3 is constructed. It is proved that these digraphs are not distinguished by the Weisfeiler–Leman algorithm and have the Weisfeiler–Leman dimension 3.",

keywords = "Cayley digraphs, Divisible design digraphs, Weisfeiler–Leman dimension",

author = "Mikhail Muzychuk and Grigory Ryabov",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Nature Japan KK 2025.",

year = "2025",

month = aug,

day = "1",

doi = "10.1007/s00373-025-02941-6",

language = "American English",

volume = "41",

journal = "Graphs and Combinatorics",

issn = "0911-0119",

publisher = "Springer Japan",

number = "4",

}

TY - JOUR

T1 - On a Family of Divisible Design Digraphs

AU - Muzychuk, Mikhail

AU - Ryabov, Grigory

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Japan KK 2025.

PY - 2025/8/1

Y1 - 2025/8/1

N2 - For every odd prime power q, a family of pairwise nonisomorphic normal arc-transitive divisible design Cayley digraphs with isomorphic neighborhood designs over a Heisenberg group of order q3 is constructed. It is proved that these digraphs are not distinguished by the Weisfeiler–Leman algorithm and have the Weisfeiler–Leman dimension 3.

AB - For every odd prime power q, a family of pairwise nonisomorphic normal arc-transitive divisible design Cayley digraphs with isomorphic neighborhood designs over a Heisenberg group of order q3 is constructed. It is proved that these digraphs are not distinguished by the Weisfeiler–Leman algorithm and have the Weisfeiler–Leman dimension 3.

KW - Cayley digraphs

KW - Divisible design digraphs

KW - Weisfeiler–Leman dimension

UR - http://www.scopus.com/inward/record.url?scp=105007762817&partnerID=8YFLogxK

U2 - 10.1007/s00373-025-02941-6

DO - 10.1007/s00373-025-02941-6

M3 - Article

SN - 0911-0119

VL - 41

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

IS - 4

M1 - 75

ER -

On a Family of Divisible Design Digraphs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this