Zhi Qiao

activity

20152026

most citedDistance-regular graphs with valency k having smallest eigenvalue at most -k/2

3 citations · 5 across the 9 of their papers we have counts for

collaborators

9 papers

math.CO2026

Sharp upper bounds on the $A_{α}$ -spectral radius of graphs

Zhen-Mu Hong, Zheng-Jiang Xia, Zhi Qiao

Let $G$ be a simple graph with degree diagonal matrix $D (G)$ and adjacency matrix $A (G)$ . The signless Laplacian matrix of $G$ is defined as $Q (G) = D (G) + A (G)$ . For a real number $α\…

math.CO2026

On the disjunctive domination numbers of the torus grid graphs

Zhi Qiao, Zheng-Jiang Xia, Zhen-Mu Hong

Let $Γ = (V, E)$ be a graph. The disjunctive domination number of $Γ$ is the minimum cardinality of a set $S \subseteq V$ such that every vertex not in $S$ is adjacent to a vertex of $…

math.CO2019★ 1 cited

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

Zhi Qiao, Yifan Jing, Jack Koolen

In 2017, Qiao and Koolen showed that for any fixed integer $D \geq 3$ , there are only finitely many such graphs with $θ_{m i n} \leq - α k$ , where $0 < α < 1$ is any fixed number. In this p…

math.CO2018

On the Cheeger constant for distance-regular graphs

Jack Koolen, Greg Markowsky, Zhi Qiao

The Cheeger constant of a graph is the smallest possible ratio between the size of a subgraph and the size of its boundary. It is well known that this constant must be at least $\f…

math.CO2017

A new characterization of the dual polar graphs

Zhi Qiao, Jack Koolen

In this paper we give a new characterization of the dual polar graphs, extending the work of Brouwer and Wilbrink on regular near polygons. Also as a consequence of our characteriz…

math.CO2016

A note on graphs with exactly two main eigenvalues

Sakander Hayat, Jack H. Koolen, Fenjin Liu +1

In this note, we consider connected graphs with exactly two main eigenvalues. We will give several constructions for them, and as a consequence we show a family of those graphs wit…

math.CO2015

Light tails and the Hermitian dual polar graphs

Jack Koolen, Zhi Qiao

Juriśič et al. conjectured that if a distance-regular graph $Γ$ with diameter $D$ at least three has a light tail, then one of the following holds: 1. $a_{1} = 0$ ; 2. $Γ$ is an antipoda…

math.CO2015★ 3 cited

Distance-regular graphs with valency k having smallest eigenvalue at most -k/2

Jack Koolen, Zhi Qiao

In this paper, we study the non-bipartite distance-regular graphs with valency k and having a smallest eigenvalue at most -k/2.

math.CO2015★ 1 cited

2-walk-regular dihedrants from group-divisible designs

Zhi Qiao, Shao Fei Du, Jack H. Koolen

In this note, we construct bipartite 2-walk-regular graphs with exactly 6 distinct eigenvalues as incidence graphs of group-divisible designs with the dual property. For many of th…

Sharp upper bounds on the Aα​-spectral radius of graphs