Non-bipartite distance-regular graphs with a small smallest eigenvalue

被引：0
|
作者：
Qiao, Zhi [1 ]
Jing, Yifan [2 ]
Koolen, Jack [3 ,4 ]
机构：
[1] Sichuan Normal Univ, Sch Math Sci, Chengdu 610068, Sichuan, Peoples R China
[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA
[3] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
[4] Chinese Acad Sci, Wen Tsun Wu Key Lab, Hefei 230026, Anhui, Peoples R China
来源：
ELECTRONIC JOURNAL OF COMBINATORICS | 2019年 / 26卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Distance-regular graphs; Smallest eigenvalue; Odd girth;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In 2017, Qiao and Koolen showed that for any fixed integer D >= 3, there are only finitely many non-bipartite distance-regular graphs with theta(min) <= -alpha k, where 0 < alpha < 1 is any fixed number. In this paper, we will study non-bipartite distance-regular graphs with relatively small theta(min) compared with k. In particular, we will show that if theta(min) is relatively close to -k then the odd girth g must be large. Also we will classify the non-bipartite distance-regular graphs with theta(min) <= -D-1/Dk for D = 4, 5.
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页数：10
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