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Sharp upper bounds on the -spectral radius of graphs
Zhen-Mu Hong, Zheng-Jiang Xia, Zhi Qiao
Let be a simple graph with degree diagonal matrix and adjacency matrix . The signless Laplacian matrix of is defined as . For a real number $α\…
On the disjunctive domination numbers of the torus grid graphs
Zhi Qiao, Zheng-Jiang Xia, Zhen-Mu Hong
Let be a graph. The disjunctive domination number of is the minimum cardinality of a set such that every vertex not in is adjacent to a vertex of $…
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 , there are only finitely many such graphs with , where is any fixed number. In this p…
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…
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…
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…