Non-Bipartite Distance-Regular Graphs with Diameters 5, 6 and a Smallest Eigenvalue

被引：0

作者：

Li, Jing ^{[1
]}

Wang, Yan ^{[2
]}

Hou, Bo ^{[1
]}

Gao, Weidong ^{[3
]}

Gao, Suogang ^{[1
]}

机构：

[1] Hebei Normal Univ, Sch Math Sci, Shijiazhuang 050024, Hebei, Peoples R China

[2] Hebei Univ Econ & Business, Coll Math & Stat, Shijiazhuang 050061, Hebei, Peoples R China

[3] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China

来源：

GRAPHS AND COMBINATORICS | 2022年 / 38卷 / 03期

关键词：

Distance-regular graphs; Valancy; Smallest eigenvalue; 2ND LARGEST;

D O I：

10.1007/s00373-022-02458-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let C be a non-bipartite distance-regular graphs with valancy k, diameter D and a smallest eigenvalue theta(min). In 2019, Qiao, Jing and Koolen classified the non-bipartite distance-regular graphs with theta(min) <= D-1/D k for D = 4; 5. In this paper, we classify the non-bipartite distance-regular graphs with theta(min) <= -D-2/D-1 k for D = 5, 6. We remark that the technique of this paper is an extension of the approach taken by Qiao, Jing and Koolen on the study of non-bipartite distance-regular graphs in 2019.

引用

页数：14

共 50 条

[21] Distance-regular extensions of strongly regular graphs with eigenvalue 2
I. N. Belousov
A. A. Makhnev
M. S. Nirova
Doklady Mathematics, 2012, 86 : 816 - 819
[22] Distance-regular extensions of strongly regular graphs with eigenvalue 2
Belousov, I. N.
Makhnev, A. A.
Nirova, M. S.
DOKLADY MATHEMATICS, 2012, 86 (03) : 816 - 819
[23] Bipartite Q-polynomial distance-regular graphs
Caughman, JS
GRAPHS AND COMBINATORICS, 2004, 20 (01) : 47 - 57
[24] A REMARK ON BIPARTITE DISTANCE-REGULAR GRAPHS OF EVEN VALENCY
NOMURA, K
GRAPHS AND COMBINATORICS, 1995, 11 (02) : 139 - 140
[25] Leaves in representation diagrams of bipartite distance-regular graphs
Lang, MS
JOURNAL OF ALGEBRAIC COMBINATORICS, 2003, 18 (03) : 245 - 254
[26] Leaves in Representation Diagrams of Bipartite Distance-Regular Graphs
Michael S. Lang
Journal of Algebraic Combinatorics, 2003, 18 : 245 - 254
[27] On bipartite Q-polynomial distance-regular graphs
Miklavic, Stefko
EUROPEAN JOURNAL OF COMBINATORICS, 2007, 28 (01) : 94 - 110
[28] 2-homogeneous bipartite distance-regular graphs
Curtin, B
DISCRETE MATHEMATICS, 1998, 187 (1-3) : 39 - 70
[29] On Bipartite Distance-Regular Cayley Graphs with Small Diameter
van Dam, Edwin R.
Jazaeri, Mojtaba
ELECTRONIC JOURNAL OF COMBINATORICS, 2022, 29 (02):
[30] Bipartite Q-Polynomial Distance-Regular Graphs
John S. Caughman IV
Graphs and Combinatorics, 2004, 20 : 47 - 57

← 1 2 3 4 5 →