Xueyi Huang

activity

20162020

most citedOn regular graphs with four distinct eigenvalues

29 citations · 80 across the 19 of their papers we have counts for

collaborators

19 papers

math.CO2020★ 1 cited

The signless Laplacian spectral radius of graphs with no intersecting triangles

Yanhua Zhao, Xueyi Huang, Hangtian Guo

Let $F_{k}$ denote the $k$ -fan consisting of $k$ triangles which intersect in exactly one common vertex, and $S_{n, k}$ the complete split graph of order $n$ consisting of a clique on…

math.CO2020

The maximum spectral radius of wheel-free graphs

Yanhua Zhao, Xueyi Huang, Huiqiu Lin

A wheel graph is a graph formed by connecting a single vertex to all vertices of a cycle. A graph is called wheel-free if it does not contain any wheel graph as a subgraph. In 2010…

math.CO2020

The $A_{α}$ -spectral radius and perfect matchings of graphs

Yanhua Zhao, Xueyi Huang, Zhiwen Wang

Let $α \in [0, 1)$ , and let $G$ be a graph of even order $n$ with $n \geq f (α)$ , where $f (α) = 10$ for $0 \leq α \leq 1/2$ , $f (α) = 14$ for $1/2 < α \leq 2/3$ and $f (α) = 5/ (1 - α)$ for $2/3 < α < 1$ . I…

math.CO2019★ 1 cited

Signless Laplacian eigenvalue problems of Nordhaus-Gaddum type

Xueyi Huang, Huiqiu Lin

Let $G$ be a graph of order $n$ , and let $q_{1} (G) \geq q_{2} (G) \geq \dots \geq q_{n} (G)$ denote the signless Laplacian eigenvalues of $G$ . Ashraf and Tayfeh-Rezaie [Electron. J. Combin. 2…

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★ 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}(…

The signless Laplacian spectral radius of graphs with no intersecting triangles

The maximum spectral radius of wheel-free graphs

The Aα​-spectral radius and perfect matchings of graphs

Signless Laplacian eigenvalue problems of Nordhaus-Gaddum type

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 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

The $A_{α}$ -spectral radius and perfect matchings of graphs

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 $- 3$