Wenqian Zhang

activity

20242026

collaborators

12 papers

math.CO2026

Spectral radius and maximum matching covered graphs with bounded matching number

Xinying Tang, Wenqian Zhang

Let $G$ be a graph. The {\em spectral radius} of $G$ is the largest eigenvalue of its {\em adjacency matrix}. A {\em matching} of $G$ is a set of disjoint edges of $G$ . The {\em ma…

math.CO2026

A lower bound of toughness of regular graphs: in terms of second largest eigenvalue

Wenqian Zhang

Let $G$ be a connected (non-complete) $d$ -regular graph with $d \geq 3$ . Let $c (G - S)$ denote the number of components of $G - S$ for any cut $S$ of $G$ . The toughness $t (G)$ of $G$ is…

math.CO2026

Some lemmas on spectral radius of graphs: including an application

Wenqian Zhang

For a graph $G$ , the spectral radius $ρ (G)$ of $G$ is the largest eigenvalue of its adjacency matrix. In this paper, we give three lammas on $ρ (G)$ when $G$ contains a spanning com…

math.CO2025

How to find all extremal graphs using symmetric subgraphs

Wenqian Zhang

Let $F$ be a finite family of graphs with $min_{F \in F} χ (F) = r + 1 \geq 3$ , where $χ (F)$ is the chromatic number of $F$ . Set $t = max_{F \in F} ∣ F ∣$ . Let ${\r…

math.CO2025

Spectral extrema of graphs forbidding a fan

Wenqian Zhang

For a graph $G$ , its spectral radius is the largest eigenvalue of its adjacency matrix. A fan $H_{ℓ}$ is a graph obtained by connecting a single vertex to all vertices of a path…

math.CO2025

Spectral conditions for graphs to contain $k$ -factors

Xinying Tang, Wenqian Zhang

Let $G$ be a graph. The spectral radius $ρ (G)$ of $G$ is the largest eigenvalue of its adjacency matrix. For an integer $k \geq 1$ , a $k$ -factor of $G$ is a $k$ -regular spanning subg…

math.CO2025

A spectral condition for Hamilton cycles in tough bipartite graphs

Lianyang Ai, Wenqian Zhang

Let $G$ be a graph. The {\em spectral radius} of $G$ is the largest eigenvalue of its adjacency matrix. For a non-complete bipartite graph $G$ with parts $X$ and $Y$ , the {\em bipa…

math.CO2025

Extremal graphs for disjoint union of vertex-critical graphs

Wenqian Zhang

For a graph $F$ , let $EX (n, F)$ be the set of $F$ -free graphs of order $n$ with the maximum number of edges. The graph $F$ is called vertex-critical, if the deletion of its so…

math.CO2025

Spectral skeletons and applications

Wenqian Zhang

For a graph $G$ , its spectral radius $ρ (G)$ is the largest eigenvalue of its adjacency matrix. Let $F$ be a finite family of graphs with $\min_{F\in \mathcal{F}}χ(F)=r+1\…

math.CO2024

A tight upper bound of spectral radius in terms of degree deviation

Wenqian Zhang

Let $G$ be a graph with $n$ vertices and $m$ edges. The spectral radius $ρ (G)$ of $G$ is the largest eigenvalue of the adjacency matrix of $G$ . As is well known, $ρ(G)\geq\frac{2m}…

math.CO2024

Eigenvalues, edge-disjoint perfect matchings and toughness of regular graphs

Wenqian Zhang

Let $G$ be a connected $d$ -regular graph of order $n$ , where $d \geq 3$ . Let $λ_{2} (G)$ be the second largest eigenvalue of $G$ . For even $n$ , we show that $G$ contains $\left\lfloor…

math.CO2024

More results on the spectral radius of graphs with no odd wheels

Wenqian Zhang

For a graph $G$ , the spectral radius $λ_{1} (G)$ of $G$ is the largest eigenvalue of its adjacency matrix. An odd wheel $W_{2 k + 1}$ with $k \geq 2$ is a graph obtained from a cycle of…

Spectral radius and maximum matching covered graphs with bounded matching number

A lower bound of toughness of regular graphs: in terms of second largest eigenvalue

Some lemmas on spectral radius of graphs: including an application

How to find all extremal graphs using symmetric subgraphs

Spectral extrema of graphs forbidding a fan

Spectral conditions for graphs to contain k-factors

A spectral condition for Hamilton cycles in tough bipartite graphs

Extremal graphs for disjoint union of vertex-critical graphs

Spectral skeletons and applications

A tight upper bound of spectral radius in terms of degree deviation

Eigenvalues, edge-disjoint perfect matchings and toughness of regular graphs

More results on the spectral radius of graphs with no odd wheels

Spectral conditions for graphs to contain $k$ -factors