On distance-regular graphs G of diameter 3 for which G??????3 is a triangle-free graph

被引：0

作者：

Makhnev, Aleksandr A. ^{[1
,2
]}

Guo, Wenbin ^{[1
,3
]}

机构：

[1] Univ Sci & Technol China, Sch Math Sci, Hefei, Peoples R China

[2] Russian Acad Sci, NN Krasovskii Inst Math & Mech, Ural Branch, Moscow, Russia

[3] Chinese Acad Sci, Inst Sci & Technol, Beijing, Peoples R China

来源：

DISCRETE MATHEMATICS AND APPLICATIONS | 2023年 / 33卷 / 04期

关键词：

distance-regular graph; triangle-free graph; triple intersection numbers;

D O I：

10.1515/dma-2023-0018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

There exist well-known distance-regular graphs G of diameter 3 for which G(3) is a triangle-free graph. An example is given by the Johnson graph 1(8, 3) with the intersection array {15, 8, 3; 1, 4, 9}. The paper is concerned with the problem of the existence of distance-regular graphs G with the intersection arrays {78, 50, 9; 1, 15, 60} and {174, 110, 18; 1, 30, 132} for which G(3) is a triangle-free graph.

引用

页码：199 / 204

页数：6

共 50 条

[41] An automorphism group of a distance-regular graph with intersection array {24, 21, 3; 1, 3, 18}
A. A. Makhnev
D. V. Paduchikh
Algebra and Logic, 2012, 51 : 319 - 332
[42] Distance regular graphs in which local subgraphs are strongly regular graphs with the second eigenvalue at most 3
A. A. Makhnev
D. V. Paduchikh
Doklady Mathematics, 2015, 92 : 568 - 571
[43] Distance regular graphs in which local subgraphs are strongly regular graphs with the second eigenvalue at most 3
Makhnev, A. A.
Paduchikh, D. V.
DOKLADY MATHEMATICS, 2015, 92 (02) : 568 - 571
[44] ARC-TRANSITIVE ANTIPODAL DISTANCE-REGULAR GRAPHS OF DIAMETER THREE RELATED TO PSLd(q)
Makhnev, A. A.
Tsiovkina, L. Y. U.
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2016, 13 : 1339 - 1345
[45] The spectral excess theorem for distance-regular graphs having distance-d graph with fewer distinct eigenvalues
M. A. Fiol
Journal of Algebraic Combinatorics, 2016, 43 : 827 - 836
[46] On Q-polynomial distance-regular graphs with a linear dependency involving a 3-clique
Mojtaba Jazaeri
Journal of Algebraic Combinatorics, 2025, 61 (3)
[47] The spectral excess theorem for distance-regular graphs having distance-d graph with fewer distinct eigenvalues
Fiol, M. A.
JOURNAL OF ALGEBRAIC COMBINATORICS, 2016, 43 (04) : 827 - 836
[48] A DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY (5, 4, 3, 3 1, 1, 1, 2) DOES NOT EXIST
FONDERFLAASS, DG
JOURNAL OF ALGEBRAIC COMBINATORICS, 1993, 2 (01) : 49 - 56
[49] An automorphism group of a distance-regular graph with intersection array {24,21,3;1,3,18}
Makhnev, A. A.
Paduchikh, D. V.
ALGEBRA AND LOGIC, 2012, 51 (04) : 319 - 332
[50] TRANSITIVE DISTANCE-REGULAR GRAPHS FROM LINEAR GROUPS L(3, q), q = 2, 3, 4, 5
Svob, Andrea
TRANSACTIONS ON COMBINATORICS, 2020, 9 (01) : 49 - 60

← 1 2 3 4 5 →