Si-Zhong Zhou

The existence of odd-even factors in 1-binding graphs

Sizhong Zhou, Qiuxiang Bian, Hongxia Liu

Let $G$ be a graph. The binding number of $G$ , denoted by $\mbox{bind}(G)$, is defined as $$ \mbox{bind}(G)=\min\left\{\frac{|N_G(S)|}{|S|}:\emptyset\neq S\subseteq V(G) \ \mbox{an…

Spectral radius and perfect k-matchings in t-connected graphs

Quanru Pan, Sizhong Zhou

A $k$ -matching of a graph $G$ is a function $f : E (G) \to {0, 1, 2, \dots, k}$ with $e \in E_{G} (v) \sum f (e) \leq k$ for each vertex $v$ of $G$ , where $E_{G} (v)$ is the set o…

Perfect matchings and $A_{α}$ -spectral radius in 1-binding graphs

Sizhong Zhou, Hongxia Liu

Let $G$ be a graph with vertex set $V (G)$ and edge set $E (G)$ . For $α \in [0, 1)$ , we use $A_{α} (G)$ and $ρ_{α} (G)$ to denote the $A_{α}$ -matrix and the $A_{α}$ -spectral radius of $G$ , respec…

Distance spectral radius and perfect matchings in graphs with given fractional property

Sizhong Zhou

A matching in a graph $G$ is a set of independent edges in $G$ . A perfect matching in a graph $G$ is a matching which saturates all the vertices of $G$ . A fractional perfect matchi…

Spectral radii and star-factors with large components

Zhiren Sun, Sizhong Zhou

Let $G$ be a connected graph with $n$ vertices. The isolated toughness of $G$ , denoted by $I (G)$ , is defined by $I(G)=\min\left\{\frac{|S|}{i(G-S)}:S\subseteq V(G) \ \mbox{and} \ i…

Sufficient conditions for even factors in graphs

Sizhong Zhou, Qiuxiang Bian, Jiancheng Wu

Let $G$ be a graph. We denote by $e (G)$ and $ρ (G)$ the size and the spectral radius of $G$ . A spanning subgraph $F$ of $G$ is called an even factor of $G$ if $d_F(v)\in\{2,4,6,\ldo…

Generalized toughness and Q-index in a graph

Sizhong Zhou

Let $G$ be a graph. We denote by $c (G)$ , $α (G)$ and $q (G)$ the number of components, the independence number and the signless Laplacian spectral radius ( $Q$ -index for short) of $G$ …

Spanning subgraphs and spectral radius in graphs

Sizhong Zhou

A spanning tree $T$ of a connected graph $G$ is a subgraph of $G$ that is a tree covers all vertices of $G$ . The leaf distance of $T$ is defined as the minimum of distances between…

Spanning k-trees, odd [1,b]-factors and spectral radius in binding graphs

Jiancheng Wu, Sizhong Zhou

The binding number of a graph $G$ , written as $\mbox{bind}(G)$, is defined by $$ \mbox{bind}(G)=\min\left\{\frac{|N_G(X)|}{|X|}:\emptyset\neq X\subseteq V(G),N_G(X)\neq V(G)\right\…

A result on spanning trees with bounded total excess

Sizhong Zhou

Let $G$ be a connected graph and $T$ a spanning tree of $G$ . Let $ρ (G)$ denote the adjacency spectral radius of $G$ . The $k$ -excess of a vertex $v$ in $T$ is defined as $\max\{0,d_…

Adjacency spectral radius and H-factors in 1-binding graphs

Sizhong Zhou, Tao Zhang, Zhiren Sun

Let $G$ be a graph, and let $H : V (G) ⟶ {{1}, {0, 2}}$ be a set-valued function. Hence, $H (v)$ equals ${1}$ or ${0, 2}$ for any $v \in V (G)$ . We let $$ H^{-1}(1)=\{…

Sufficient conditions for a graph with minimum degree to be k-critical with respect to [1,b]-odd factor

Sizhong Zhou

A spanning subgraph $F$ of a graph $G$ is called a $[1, b]$ -odd factor if $b \equiv 1$ (mod 2) and $d_{F} (v) \in {1, 3, \dots, b}$ for every $v \in V (G)$ . A graph $G$ of order $n \geq k + 2$ …

An Aα-spectral radius for the existence of {P3, P4, P5}-factors in graphs

Yuli Zhang, Sizhong Zhou

Let $G$ be a connected graph of order $n$ with $n \geq 25$ . A ${P_{3}, P_{4}, P_{5}}$ -factor is a spanning subgraph $H$ of $G$ such that every component of $H$ is isomorphic to an element…

A spectral condition for spanning trees with restricted degrees in bipartite graphs

Jiancheng Wu, Sizhong Zhou, Hongxia Liu

Let $G$ be a graph and $T$ be a spanning tree of $G$ . We use $Q (G) = D (G) + A (G)$ to denote the signless Laplacian matrix of $G$ , where $D (G)$ is the diagonal degree matrix of $G$ and…

Some sufficient conditions for graphs to have component factors

Sizhong Zhou

Let $G$ denote a graph and $k \geq 2$ be an integer. A ${K_{1, 1}, K_{1, 2}, \dots, K_{1, k}, T (2 k + 1)}$ -factor of $G$ is a spanning subgraph, whose every connected component is…

Aα-spectral radius and path-factor covered graphs

Sizhong Zhou, Hongxia Liu, Qiuxiang Bian

Let $α \in [0, 1)$ , and let $G$ be a connected graph of order $n$ with $n \geq f (α)$ , where $f (α) = 14$ for $α \in [0, \frac{1}{2}]$ , $f (α) = 17$ for $α \in (\frac{1}{2}, \frac{2}{3}]$ , $f(α)=20…

Toughness and Aα-spectral radius in graphs

Sizhong Zhou, Yuli Zhang, Tao Zhang +1

Let $α \in [0, 1)$ , and let $G$ be a connected graph of order $n$ with $n \geq f (α)$ , where $f (α) = 6$ for $α \in [0, \frac{2}{3}]$ and $f (α) = \frac{4}{1 - α}$ for $α \in (\frac{2}{3}, 1)$ . A gra…