Xiaogang Liu

activity

20102026

most citedSpectra of subdivision-vertex and subdivision-edge neighbourhood coronae

75 citations · 297 across the 21 of their papers we have counts for

collaborators

22 papers

math.CO2026

Localization of spectral Turán theorems for signed graphs

Linfeng Xie, Xiaogang Liu

In this paper, we extend localized Turán theorems to signed graphs and study the corresponding spectral Turán problems. Firstly, we establish a vertex-localized Turán-type inequali…

math.CO2023

Fractional revival on semi-Cayley graphs over abelian groups

Jing Wang, Ligong Wang, Xiaogang Liu

In this paper, we investigate the existence of fractional revival on semi-Cayley graphs over finite abelian groups. We give some necessary and sufficient conditions for semi-Cayley…

math.CO2022

Fractional revival on Cayley graphs over abelian groups

Jing Wang, Ligong Wang, Xiaogang Liu

In this paper, we investigate the existence of fractional revival on Cayley graphs over finite abelian groups. We give a necessary and sufficient condition for Cayley graphs over f…

quant-ph2022

Laplacian state transfer in vertex complemented coronas

Qiang Wang, Xiaogang Liu

In this paper, we investigate the existence of Laplacian perfect state transfer and Laplacian pretty good state transfer in vertex complemented coronas. We prove that there is no L…

math.CO2020

Perfect state transfer in NEPS of complete graphs

Yipeng Li, Xiaogang Liu, Shenggui Zhang +1

Perfect state transfer in graphs is a concept arising from quantum physics and quantum computing. Given a graph $G$ with adjacency matrix $A_{G}$ , the transition matrix of $G$ with r…

cs.IT2019

Necessities and sufficiencies of a class of permutation polynomials over finite fields

Xiaogang Liu

For the finite field $F_{2^{3 m}}$ , permutation polynomials of the form $(x^{2^{m}} + x + δ)^{s} + c x$ are studied. Necessary and sufficient conditions are given for the polynomial…

cs.IT2019★ 3 cited

Further results on some classes of permutation polynomials over finite fields

Xiaogang Liu

Let $F_{q}$ denote the finite fields with $q$ elements. The permutation behavior of several classes of infinite families of permutation polynomials over finite fields have b…

cs.IT2019★ 3 cited

Constructions and necessities of some permutation polynomials

Xiaogang Liu

Permutation polynomials over finite fields have important applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, etc. In t…

cs.IT2019★ 2 cited

Some results about permutation properties of a kind of binomials over finite fields

Xiaogang Liu

Permutation polynomials have many applications in finite fields theory, coding theory, cryptography, combinatorial design, communication theory, and so on. Permutation binomials of…

math.CO2018★ 50 cited

Eigenvalues of Cayley graphs

Xiaogang Liu, Sanming Zhou

We survey some of the known results on eigenvalues of Cayley graphs and their applications, together with related results on eigenvalues of Cayley digraphs and generalizations of C…

math.CO2017★ 39 cited

On the $A_{α}$ -characteristic polynomial of a graph

Xiaogang Liu, Shunyi Liu

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

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.CO2015★ 16 cited

Quadratic unitary Cayley graphs of finite commutative rings

Xiaogang Liu, Sanming Zhou

The purpose of this paper is to study spectral properties of a family of Cayley graphs on finite commutative rings. Let $R$ be such a ring and $R^{\times}$ its set of units. Let $Q_R…

math.NT2015

On the Lower Bound of the Divisibility of Exponential Sums in Binomial Case

Xiaogang Liu

Francis Castro, et al [2] computed the exact divisibility of families of exponential sums associated to binomials $F (X) = a X^{d_{1}} + b X^{d_{2}}$ over $F_{p}$ , and a conjecture…

math.CO2014★ 5 cited

Laplacian spectral characterization of dumbbell graphs and theta graphs

Xiaogang Liu, Pengli Lu

Let $P_{n}$ and $C_{n}$ denote the path and cycle on $n$ vertices respectively. The dumbbell graph, denoted by $D_{p, k, q}$ , is the graph obtained from two cycles $C_{p}$ , $C_{q}$ and a pat…

math.CO2012★ 75 cited

Spectra of subdivision-vertex and subdivision-edge neighbourhood coronae

Xiaogang Liu, Pengli Lu

Let $G = (V (G), E (G))$ be a graph with vertex set $V (G)$ and edge set $E (G)$ . The subdivision graph $S (G)$ of a graph $G$ is the graph obtained by inserting a new vertex int…

math.CO2012★ 36 cited

Spectra of subdivision-vertex join and subdivision-edge join of two graphs

Xiaogang Liu, Zuhe Zhang

The subdivision graph $S (G)$ of a graph $G$ is the graph obtained by inserting a new vertex into every edge of $G$ . Let $G_{1}$ and $G_{2}$ be two vertex disjoint graphs. The…

math.CO2012★ 47 cited

Spectra of the neighbourhood corona of two graphs

Xiaogang Liu, Sanming Zhou

Given simple graphs $G_{1}$ and $G_{2}$ , the neighbourhood corona of $G_{1}$ and $G_{2}$ , denoted $G_{1} ⋆ G_{2}$ , is the graph obtained by taking one copy of $G_{1}$ and $∣ V (G_{1}) ∣$ copies of…

math.CO2012

Laplacian spectral characterization of some double starlike trees

Pengli Lu, Xiaogang Liu

A tree is called double starlike if it has exactly two vertices of degree greater than two. Let $H (p, n, q)$ denote the double starlike tree obtained by attaching $p$ pendant vertice…

math.CO2012★ 3 cited

Spectral characterizations of propeller graphs

Xiaogang Liu, Sanming Zhou

A propeller graph is obtained from an $\infty$ -graph by attaching a path to the vertex of degree four, where an $\infty$ -graph consists of two cycles with precisely one common vert…

math.CO2012

Spectral properties of unitary Cayley graphs of finite commutative rings

Xiaogang Liu, Sanming Zhou

Let $R$ be a finite commutative ring. The unitary Cayley graph of $R$ , denoted $G_{R}$ , is the graph with vertex set $R$ and edge set $a, b : a, b \in R, a - b \in R^{\times}$ , where $R^\t…

math.CO2010★ 18 cited

Laplacian spectral characterization of some graph products

Suijie Wang, Xiaogang Liu

This paper studies the Laplacian spectral characterization of some graph products. We consider a class of connected graphs: $G = G : ∣ E G ∣ \leq ∣ V G ∣ + 1$ , and characterize all…

Localization of spectral Turán theorems for signed graphs

Fractional revival on semi-Cayley graphs over abelian groups

Fractional revival on Cayley graphs over abelian groups

Laplacian state transfer in vertex complemented coronas

Perfect state transfer in NEPS of complete graphs

Necessities and sufficiencies of a class of permutation polynomials over finite fields

Further results on some classes of permutation polynomials over finite fields

Constructions and necessities of some permutation polynomials

Some results about permutation properties of a kind of binomials over finite fields

Eigenvalues of Cayley graphs

On the Aα​-characteristic polynomial of a graph

Graphs determined by their Aα​-spectra

Quadratic unitary Cayley graphs of finite commutative rings

On the Lower Bound of the Divisibility of Exponential Sums in Binomial Case

Laplacian spectral characterization of dumbbell graphs and theta graphs

Spectra of subdivision-vertex and subdivision-edge neighbourhood coronae

Spectra of subdivision-vertex join and subdivision-edge join of two graphs

Spectra of the neighbourhood corona of two graphs

Laplacian spectral characterization of some double starlike trees

Spectral characterizations of propeller graphs

Spectral properties of unitary Cayley graphs of finite commutative rings

Laplacian spectral characterization of some graph products

On the $A_{α}$ -characteristic polynomial of a graph

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