Ruifang Liu

activity

20142023

k

-factors and spanning trees of graphs

1 citations · 2 across the 19 of their papers we have counts for

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20 papers · 1 filter

math.CO2023★ 1 cited

Sufficient conditions for $k$ -factors and spanning trees of graphs

Guoyan Ao, Ruifang Liu, Jinjiang Yuan +2

For any integer $k \geq 1,$ a graph $G$ has a $k$ -factor if it contains a $k$ -regular spanning subgraph. In this paper we prove a sufficient condition in terms of the number of $r$ -c…

math.CO2023

Spectral radius, fractional $[a, b]$ -factor and ID-factor-critical graphs

Ao Fan, Ruifang Liu, Guoyan Ao

Let $G$ be a graph and $h : E (G) \to [0, 1]$ be a function. For any two positive integers $a$ and $b$ with $a \leq b$ , a fractional $[a, b]$ -factor of $G$ with the indicator fun…

math.CO2023

Fractional matching, factors and spectral radius in graphs involving minimum degree

Jing Lou, Ruifang Liu, Guoyan Ao

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~ \mbox{…

math.CO2022

Spectral radius and spanning trees of graphs

Guoyan Ao, Ruifang Liu, Jinjiang Yuan

For integer $k \geq 2,$ a spanning $k$ -ended-tree is a spanning tree with at most $k$ leaves. Motivated by the closure theorem of Broersma and Tuinstra [Independence trees and Hamilt…

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…

math.CO2022

An improvement of sufficient condition for $k$ -leaf-connected graphs

Tingyan Ma, Guoyan Ao, Ruifang Liu +2

For integer $k \geq 2,$ a graph $G$ is called $k$ -leaf-connected if $∣ V (G) ∣ \geq k + 1$ and given any subset $S \subseteq V (G)$ with $∣ S ∣ = k,$ $G$ always has a spanning tree $T$ such that…

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

A spectral Erdős-Pósa Theorem

Zhai Mingqing, Liu Ruifang

A set of cycles is called independent if no two of them have a common vertex. Let $S_{n, 2 k - 1}$ be the complete split graph, which is the join of a clique of size $2 k - 1$ with an in…

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.CO2019

Vertex-connectivity and $Q$ -index of graphs with fixed girth

Huicai Jia, Hong-Jian Lai, Ruifang Liu +1

Let $q (G)$ denote the $Q$ -index of a graph $G$ , which is the largest signless Laplacian eigenvalue of $G$ . We prove best possible upper bounds of $q (G)$ and best possible lower bou…

math.CO2018

A note on eigenvalues and Hamiltoinan properties of $k$ -connected graphs

Huicai Jia, Ruifang Liu, Hong-Jian Lai

Let $λ_{1} (G)$ and $μ_{1} (G)$ denote the spectral radius and the Laplacian spectral radius of a graph $G$ , respectively. Li in [Electronic J. Linear Algebra 34 (2018) 389-392] prov…

math.CO2018

Spanning tree packing, edge-connectivity and eigenvalues of graphs with given girth

Ruifang Liu, Hong-Jian Lai, Yingzhi Tian

Let $τ (G)$ and $κ^{'} (G)$ denote the edge-connectivity and the spanning tree packing number of a graph $G$ , respectively. Proving a conjecture initiated by Cioaba and Wong, Liu et al.…

math.CO2017

Signless Laplacian spectral radius and fractional matchings in graphs

Ruifang Liu, Yu Lu

A {\it fractional matching} of a graph $G$ is a function $f$ giving each edge a number in $[0, 1]$ so that $\sum_{e \in Γ (v)} f (e) \leq 1$ for each $v \in V (G)$ , where $Γ (v)$ is the set…

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…

Sufficient conditions for k-factors and spanning trees of graphs

Spectral radius, fractional [a,b]-factor and ID-factor-critical graphs

Fractional matching, factors and spectral radius in graphs involving minimum degree

Spectral radius and spanning trees of graphs

Laplacian eigenvalue distribution, diameter and domination number of trees

An improvement of sufficient condition for k-leaf-connected 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

A spectral Erdős-Pósa Theorem

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

Vertex-connectivity and Q-index of graphs with fixed girth

A note on eigenvalues and Hamiltoinan properties of k-connected graphs

Spanning tree packing, edge-connectivity and eigenvalues of graphs with given girth

Signless Laplacian spectral radius and fractional matchings in 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

Sufficient conditions for $k$ -factors and spanning trees of graphs

Spectral radius, fractional $[a, b]$ -factor and ID-factor-critical graphs

An improvement of sufficient condition for $k$ -leaf-connected graphs

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

Vertex-connectivity and $Q$ -index of graphs with fixed girth

A note on eigenvalues and Hamiltoinan properties of $k$ -connected graphs

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