Qiongxiang Huang

activity

20162019

most citedOn regular graphs with four distinct eigenvalues

29 citations · 82 across the 18 of their papers we have counts for

collaborators

18 papers

math.CO2019

On joins of a clique and a co-clique as star complements in regular graphs

Yuhong Yang, Jianfeng Wang, Qiongxiang Huang +1

In this paper we consider $r$ -regular graphs $G$ that admit the vertex set partition such that one of the induced subgraphs is the join of an $s$ -vertex clique and a $t$ -vertex co-…

math.CO2018

Infinite classes of strongly regular graphs derived from $G L (n, F_{2})$

Lu Lu, Qiongxiang Huang, Jiangxia Hou

It is known that the automorphism group of the elementary abelian $2$ -group $Z_{2}^{n}$ is isomorphic to the general linear group $G L (n, F_{2})$ of degree $n$ over $F_{2}$ . Let $W$ be the c…

math.CO2018★ 2 cited

The spectrum and automorphism group of the set-inclusion graph

Xueyi Huang, Qiongxiang Huang, Jianfeng Wang

Let $n$ , $k$ and $l$ be integers with $1 \leq k < l \leq n - 1$ . The set-inclusion graph $G (n, k, l)$ is the graph whose vertex set consists of all $k$ - and $l$ -subsets of $[n]=\{1,2,\ldot…

math.CO2018★ 1 cited

The second eigenvalue of some normal Cayley graphs of high transitive groups

Xueyi Huang, Qiongxiang Huang, Sebastian M. Cioabă

Let $Γ$ be a finite group acting transitively on $[n] = {1, 2, \dots, n}$ , and let $G = Cay (Γ, T)$ be a Cayley graph of $Γ$ . The graph $G$ is called normal if $T$ is closed und…

math.CO2018

A complete characterization of graphs with exactly two positive eigenvalues

Fang Duan, Qiongxiang Huang, Xueyi Huang +2

In 1977 Smith characterized graphs with exactly one positive eigenvalue. Since then, many particular results related to graphs with exactly two positive eigenvalues have emerged. I…

math.CO2018

On graphs with exactly two positive eigenvalues

Fang Duan, Qiongxiang Huang, Xueyi Huang

The inertia of a graph $G$ is defined to be the triplet $I n (G) = (p (G), n (G),$ $η (G))$ , where $p (G)$ , $n (G)$ and $η (G)$ are the numbers of positive, negative and zero eigenvalues…

math.CO2017★ 13 cited

The second largest eigenvalues of some Cayley graphs on alternating groups

Xueyi Huang, Qiongxiang Huang

Let $A_{n}$ denote the alternating group of degree $n$ with $n \geq 3$ . The alternating group graph $A G_{n}$ , extended alternating group graph $E A G_{n}$ and complete alternating group gra…

math.CO2017

Graphs with at most three distance eigenvalues different from $- 1$ and $- 2$

Xueyi Huang, Qiongxiang Huang, Lu Lu

Let $G$ be a connected graph on $n$ vertices, and let $D (G)$ be the distance matrix of $G$ . Let $\partial_{1} (G) \geq \partial_{2} (G) \geq \dots \geq \partial_{n} (G)$ denote the eigenvalues of $…

math.CO2017

On graphs with $m (\partial_{1}^{L}) = n - 3$

Lu Lu, Qiongxiang Huang, Xueyi Huang

Let $\partial_{1}^{L} \geq \partial_{2}^{L} \geq \dots \geq \partial_{n}^{L}$ be the distance Laplacian eigenvalues of a connected graph $G$ and $m (\partial_{i}^{L})$ the multiplicity of $\partial_{i}^{L}$ . I…

math.CO2016

Enumerating Cayley (di-)graphs on dihedral groups

Xueyi Huang, Qiongxiang Huang

Let $p$ be an odd prime, and $D_{2 p} = ⟨ τ, σ ∣ τ^{p} = σ^{2} = e, σ τ σ = τ^{- 1} ⟩$ the dihedral group of order $2 p$ . In this paper, we provide the number of (connected) Cayley (di-)…

math.CO2016

On graphs with three or four distinct normalized Laplacian eigenvalues

Xueyi Huang, Qiongxiang Huang

In this paper, we characterize all connected graphs with exactly three distinct normalized Laplacian eigenvalues of which one is equal to $1$ , determine all connected bipartite gra…

math.CO2016★ 5 cited

Enumeration of cubic Cayley graphs on dihedral groups

Xueyi Huang, Qiongxiang Huang, Lu Lu

Let $p$ be an odd prime, and $D_{2 p} = ⟨ a, b ∣ a^{p} = b^{2} = 1, bab = a^{- 1} ⟩$ the dihedral group of order $2 p$ . In this paper, we completely classify the cubic Cayley graphs on…

math.CO2016

Automorphism groups of a class of cubic Cayley graphs on symmetric groups

Xueyi Huang, Qiongxiang Huang, Lu Lu

Let $S_{n}$ denote the symmetric group of degree $n$ with $n \geq 3$ . Set $S = {c_{n} = (12 \dots n), c_{n}^{- 1}, (12)}$ . Let $Γ_{n} = Cay (S_{n}, S)$ be the Cayley graph on $S_{n}$ with…

math.CO2016★ 4 cited

The existence of the graphs that have exactly two main eigenvalues

Lin Chen, Qiongxiang Huang

An eigenvalue of a graph $G$ is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. It is well known that a graph $G$ has exactly two m…

math.CO2016★ 20 cited

The graphs with exactly two distance eigenvalues different from $- 1$ and $- 3$

Lu Lu, Qiongxiang Huang, Xueyi Huang

In this paper, we completely characterize the graphs with third largest distance eigenvalue at most $- 1$ and smallest distance eigenvalue at least $- 3$ . In particular, we determine…

math.CO2016

Integral Cayley Graphs over Dihedral Groups

Lu Lu, Qiongxiang Huang, Xueyi Huang

In this paper, we give a necessary and sufficient condition for the integrality of Cayley graphs over the dihedral group $D_{n} = ⟨ a, b ∣ a^{n} = b^{2} = 1, bab = a^{- 1} ⟩$ . Moreover…

math.CO2016★ 8 cited

Automorphism group of the complete alternating group graph

Xueyi Huang, Qiongxiang Huang

Let $S_{n}$ and $A_{n}$ denote the symmetric group and alternating group of degree $n$ with $n \geq 3$ , respectively. Let $S$ be the set of all $3$ -cycles in $S_{n}$ . The \emph{complete a…

math.CO2016★ 29 cited

On regular graphs with four distinct eigenvalues

Xueyi Huang, Qiongxiang Huang

Let $G (4, 2)$ be the set of connected regular graphs with four distinct eigenvalues in which exactly two eigenvalues are simple, $G (4, 2, - 1)$ (resp. $\mathcal{G}(…

On joins of a clique and a co-clique as star complements in regular graphs

Infinite classes of strongly regular graphs derived from GL(n,F2​)

The spectrum and automorphism group of the set-inclusion graph

The second eigenvalue of some normal Cayley graphs of high transitive groups

A complete characterization of graphs with exactly two positive eigenvalues

On graphs with exactly two positive eigenvalues

The second largest eigenvalues of some Cayley graphs on alternating groups

Graphs with at most three distance eigenvalues different from −1 and −2

On graphs with m(∂1L​)=n−3

Enumerating Cayley (di-)graphs on dihedral groups

On graphs with three or four distinct normalized Laplacian eigenvalues

Enumeration of cubic Cayley graphs on dihedral groups

Automorphism groups of a class of cubic Cayley graphs on symmetric groups

The existence of the graphs that have exactly two main eigenvalues

The graphs with exactly two distance eigenvalues different from −1 and −3

Integral Cayley Graphs over Dihedral Groups

Automorphism group of the complete alternating group graph

On regular graphs with four distinct eigenvalues

Infinite classes of strongly regular graphs derived from $G L (n, F_{2})$

Graphs with at most three distance eigenvalues different from $- 1$ and $- 2$

On graphs with $m (\partial_{1}^{L}) = n - 3$

The graphs with exactly two distance eigenvalues different from $- 1$ and $- 3$