Jie Xue

activity

20142026

A_{α}

-spectra of graphs

53 citations · 63 across the 16 of their papers we have counts for

collaborators

17 papers

math.CO2026

Hamiltonian paths in the permutation digraphs $P (n, n - 2)$

Jiaxin Guo, Ming Duan, Jie Xue

For $1 \leq k < n$ , let $P (n, k)$ be the directed overlap graph whose vertices are the $k$ -permutations of $[n]$ and whose arcs are the $(k + 1)$ -permutations. Isaak proved that $P(n,n-2…

cs.DS2023

Efficient Approximation for Subgraph-Hitting Problems in Sparse Graphs and Geometric Intersection Graphs

Zdeněk Dvořák, Daniel Lokshtanov, Fahad Panolan +3

We investigate a fundamental vertex-deletion problem called (Induced) Subgraph Hitting: given a graph $G$ and a set $F$ of forbidden graphs, the goal is to compute a mini…

math.CO2022

Laplacian eigenvalue distribution, diameter and domination number of trees

Jiaxin Guo, Jie Xue, Ruifang Liu

For a graph $G$ with domination number $γ$ , Hedetniemi, Jacobs and Trevisan [European Journal of Combinatorics 53 (2016) 66-71] proved that $m_{G} [0, 1) \leq γ$ , where $m_{G} [0, 1)$ m…

cs.CG2022

A Framework for Approximation Schemes on Disk Graphs

Daniel Lokshtanov, Fahad Panolan, Saket Saurabh +2

We initiate a systematic study of approximation schemes for fundamental optimization problems on disk graphs, a common generalization of both planar graphs and unit-disk graphs. Ou…

math.CO2022

Maxima of spectral radius of irregular graphs with given maximum degree

Jie Xue, Ruifang Liu

Let $λ^{*}$ be the maximum spectral radius of connected irregular graphs on $n$ vertices with maximum degree $Δ$ . Liu, Shen and Wang (2007) conjectured that $\lim_{n\rightarrow \in…

math.CO2022

Maxima of the $Q$ -index of non-bipartite $C_{3}$ -free graphs

Ruifang Liu, Lu Miao, Jie Xue

A classic result in extremal graph theory, known as Mantel's theorem, states that every non-bipartite graph of order $n$ with size $m > ⌊ \frac{n ^{2}}{4} ⌋$ contains a tri…

math.CO2022

Cubic bipartite graphs with minimum spectral gap

Ruifang Liu, Jie Xue

The difference between the two largest eigenvalues of the adjacency matrix of a graph $G$ is called the spectral gap of $G .$ If $G$ is a regular graph, then its spectral gap is equ…

math.CO2022

The maximum spectral radius of irregular bipartite graphs

Jie Xue, Ruifang Liu, Jiaxin Guo +1

A bipartite graph is subcubic if it is an irregular bipartite graph with maximum degree three. In this paper, we prove that the asymptotic value of maximum spectral radius over sub…

math.CO2020

A spectral extremal problem on graphs with given size and matching number

Mingqing Zhai, Jie Xue, Ruifang Liu

Brualdi and Hoffman (1985) proposed the problem of determining the maximal spectral radius of graphs with given size. In this paper, we consider the Brualdi-Hoffman type problem of…

math.CO2020

Fractional matching number and spectral radius of nonnegative matrix of graphs

Ruifang Liu, Hong-Jian Lai, Litao Guo +1

A fractional matching of a graph $G$ is a function $f : E (G) \to [0, 1]$ such that for any $v \in V (G)$ , $\sum_{e \in E_{G} (v)} f (e) \leq 1$ where $E_{G} (v) = {e \in E (G) : e$ is incident wit…

math.CO2018

A note on the $A_{α}$ -spectral radius of graphs

Huiqiu Lin, Xing Huang, Jie Xue

Let $G$ be a graph with adjacency matrix $A (G)$ and let $D (G)$ be the diagonal matrix of the degrees of $G$ . For any real $α \in [0, 1]$ , Nikiforov [Merging the $A$ - and $Q$ -spectral…

math.CO2017

Graphs determined by their $A_{α}$ -spectra

Huiqiu Lin, Xiaogang Liu, Jie Xue

Let $G$ be a graph with $n$ vertices, and let $A (G)$ and $D (G)$ denote respectively the adjacency matrix and the degree matrix of $G$ . Define $A_{α} (G) = α D (G) + (1 - α) A (G)$ for any r…

math.CO2017★ 53 cited

On the $A_{α}$ -spectra of graphs

Huiqiu Lin, Jie Xue, Jinlong Shu

Let $G$ be a graph with adjacency matrix $A (G)$ and let $D (G)$ be the diagonal matrix of the degrees of $G$ . For any real $α \in [0, 1]$ , Nikiforov \cite{VN1} defined the matrix $A_α…

math.CO2017★ 9 cited

More results on the distance (signless) Laplacian eigenvalues of graphs

Jie Xue, Huiqiu Lin, Kinkar Ch. Das +1

Let $G$ be a connected graph with vertex set $V (G)$ and edge set $E (G)$ . Let $T r (G)$ be the diagonal matrix of vertex transmissions of $G$ and $D (G)$ be the distance matrix of $G$ .…

math.CO2015

Graphs with small diameter determined by their $D$ -spectra

Ruifang Liu, Jie Xue

Let $G$ be a connected graph with vertex set $V (G) = {v_{1}, v_{2}, ..., v_{n}}$ . The distance matrix $D (G) = (d_{ij})_{n \times n}$ is the matrix indexed by the vertices of $G,$ where $…

math.CO2015★ 1 cited

On the second largest distance eigenvalue of a graph

Ruifang Liu, Jie Xue, Litao Guo

Let $G$ be a simple connected graph of order $n$ and $D (G)$ be the distance matrix of $G .$ Suppose that $λ_{1} (D (G)) \geq λ_{2} (D (G)) \geq \dots \geq λ_{n} (D (G))$ are the distance spect…

math.CO2014

Sufficient spectral conditions on Hamiltonian and traceable graphs

Ruifang Liu, Wai Chee Shiu, Jie Xue

In this paper, we give sufficient conditions on the spectral radius for a bipartite graph to Hamiltonian and traceable, which expand the results of Lu, Liu and Tian (2012) [10]. Fu…

Hamiltonian paths in the permutation digraphs P(n,n−2)

Efficient Approximation for Subgraph-Hitting Problems in Sparse Graphs and Geometric Intersection Graphs

Laplacian eigenvalue distribution, diameter and domination number of trees

A Framework for Approximation Schemes on Disk Graphs

Maxima of spectral radius of irregular graphs with given maximum degree

Maxima of the Q-index of non-bipartite C3​-free graphs

Cubic bipartite graphs with minimum spectral gap

The maximum spectral radius of irregular bipartite graphs

A spectral extremal problem on graphs with given size and matching number

Fractional matching number and spectral radius of nonnegative matrix of graphs

A note on the Aα​-spectral radius of graphs

Graphs determined by their Aα​-spectra

On the Aα​-spectra of graphs

More results on the distance (signless) Laplacian eigenvalues of graphs

Graphs with small diameter determined by their D-spectra

On the second largest distance eigenvalue of a graph

Sufficient spectral conditions on Hamiltonian and traceable graphs

Hamiltonian paths in the permutation digraphs $P (n, n - 2)$

Maxima of the $Q$ -index of non-bipartite $C_{3}$ -free graphs

A note on the $A_{α}$ -spectral radius of graphs

Graphs determined by their $A_{α}$ -spectra

On the $A_{α}$ -spectra of graphs

Graphs with small diameter determined by their $D$ -spectra