1School of Mathematical Sciences, Sichuan Normal University, 610068, Sichuan, PR China 2Department of Mathematics, University of Illinois at Urbana Champaign, Urbana, IL, 61801, USA
The electronic journal of combinatorics, Tome 26 (2019) no. 2
In 2017, Qiao and Koolen showed that for any fixed integer $D\geqslant 3$, there are only finitely many such graphs with $\theta_{\min}\leqslant -\alpha k$, 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 $\theta_{\min} \leqslant -\frac{D-1}{D}k$ for $D =4,5$.
1
School of Mathematical Sciences, Sichuan Normal University, 610068, Sichuan, PR China
2
Department of Mathematics, University of Illinois at Urbana Champaign, Urbana, IL, 61801, USA
@article{10_37236_8361,
author = {Zhi Qiao and Yifan Jing and Jack Koolen},
title = {Non-bipartite distance-regular graphs with a small smallest eigenvalue},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {2},
doi = {10.37236/8361},
zbl = {1416.05096},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8361/}
}
TY - JOUR
AU - Zhi Qiao
AU - Yifan Jing
AU - Jack Koolen
TI - Non-bipartite distance-regular graphs with a small smallest eigenvalue
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/8361/
DO - 10.37236/8361
ID - 10_37236_8361
ER -
%0 Journal Article
%A Zhi Qiao
%A Yifan Jing
%A Jack Koolen
%T Non-bipartite distance-regular graphs with a small smallest eigenvalue
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/8361/
%R 10.37236/8361
%F 10_37236_8361
Zhi Qiao; Yifan Jing; Jack Koolen. Non-bipartite distance-regular graphs with a small smallest eigenvalue. The electronic journal of combinatorics, Tome 26 (2019) no. 2. doi: 10.37236/8361
