Ligong Wang

Spectral extremal problems for fractional $I D$ - $[a, b]$ -factor-critical graphs

Zengzhao Xu, Ligong Wang, Weige Xi

A factor of a graph is essentially a specific type spanning subgraph. In recent years, the spectral extremal problem of characterizing the existence of graph factors via eigenvalue…

Spectral radius conditions for edge-disjoint spanning trees in $(k + c)$ -edge-connected graphs

Yongbin Gao, Ligong Wang

Let $τ (G)$ denote the spanning tree packing number of a graph $G$ . Recently, Zhang and Fan [J. Graph Theory 112 (2) (2026) 128--144] posed the problem of finding a tight spectral r…

Distance spectral radius conditions for perfect $k$ -matching, generalized factor-criticality (bicriticality) and $k$ - $d$ -criticality of graphs

Kexin Yang, Ligong Wang, Zhenhao Zhang

Let $G$ be a simple connected graph with vertex set $V (G)$ and edge set $E (G)$ . A $k$ -matching of a graph $G$ is a function $f : E (G) \to {0, 1, \dots, k}$ satisfying $\sum_{…

Size conditions and spectral conditions for generalized factor-critical (bicritical) graphs and $k$ - $d$ -critical graphs

Zhenhao Zhang, Ligong Wang

Let $\mbox{odd}(G)$ and $i (G)$ denote the number of nontrivial odd components and the number of isolated vertices of a graph $G$ , respectively. The $k$ -Berge-Tutte-formula of a gra…

Distance spectral radius conditions for edge-disjoint spanning trees and a forest with constraints

Yongbin Gao, Ligong Wang

Let $k \geq 2$ be a positive integer and let $G$ be a simple graph of order $n$ with minimum degree $δ$ . A graph $G$ is said to have property $P (k, d)$ if it contains $k$ edge-disjoi…

Laplacian eigenvalue conditions for edge-disjoint spanning trees and a forest with constraints

Yongbin Gao, Ligong Wang

Let $k$ be a positive integer and let $G$ be a simple graph of order $n$ with minimum degree $δ$ . A graph $G$ is said to have property $P (k, d)$ if it contains $k$ edge-disjoint sp…

Spectral extremal problems for $(a, b, k)$ -critical and fractional $(a, b, k)$ -critical graphs

Zengzhao Xu, Ligong Wang, Weige Xi

A factor of a graph is essentially a specific type spanning subgraph. The study of characterizing the existence of $[a, b]$ -factors based on eigenvalue conditions can be traced bac…

Spectral radius and size conditions for fractional $(a, b, m)$ -covered graphs

Zengzhao Xu, Ligong Wang, Weige Xi

A fractional $(a, b, m)$ -covered graph is a generalization of the concept of a fractional $[a, b]$ -covered graph. For any $H \subseteq G$ with edge set $∣ E (H) ∣ = m$ , if there exists a…

Tricyclic graphs for which the second largest distance eigenvalue less than $- \frac{1}{2}$

Kexin Yang, Ligong Wang

Let $G$ be a simple connected graph with vertex set $V (G) = {v_{1}, v_{2}, \dots, v_{n}}$ . The distance $d_{G} (v_{i}, v_{j})$ between two vertices $v_{i}$ and $v_{j}$ of $G$ is the length of…

On the distance signless Laplacian spectral radius, fractional matching and factors of graphs

Z. H. Zhang, L. G. Wang

The distance signless Laplacian matrix of a graph $G$ is define as $Q (G) =$ Tr $(G) + D (G)$ , where Tr $(G)$ and $D (G)$ are the diagonal matrix of vertex transmissions and the distance ma…

Ordering digraphs with maximum outdegrees by their $A_{α}$ spectral radius

Zengzhao Xu, Weige Xi, Ligong Wang

Let $G$ be a strongly connected digraph with $n$ vertices and $m$ arcs. For any real $α \in [0, 1]$ , the $A_{α}$ matrix of a digraph $G$ is defined as $A_{α} (G) = α D (G) + (1 - α) A (G),$ where…

Maximizing the signless Laplacian spectral radius of some theta graphs

Yuxiang Liu, Ligong Wang

Let $Q (G) = D (G) + A (G)$ be the signless Laplacian matrix of a simple graph $G$ , where $D (G)$ and $A (G)$ are the degree diagonal matrix and the adjacency matrix of $G$ , respectively. T…

Extension on spectral extrema of gem-free graph with given size

Yuxiang Liu, Ligong Wang

A graph $G$ is $F$ -free if $G$ does not contain $F$ as a subgraph. Let $G (m, F)$ denote the family of $F$ -free graphs with $m$ edges and without isolated vertices. Let $S…

Maxima of the $Q$ -index of 2 leaves-free graphs with given size

Yuxiang Liu, Ligong Wang, Xiaolong Jia

The $Q$ -index of graph $G$ is the largest eigenvalue of the signless Laplacian matrix of $G$ . Wang [Discrete Appl. Math. 356(2024)] proved the sharp upper bounds on the $Q$ -index o…

On the $D_{α}$ spectral radius of non-transmission regular graphs

Zengzhao Xu, Weige Xi, Ligong Wang

Let $G$ be a connected graph with order $n$ and size $m$ . Let $D (G)$ and $T r (G)$ be the distance matrix and diagonal matrix with vertex transmissions of $G$ , respectively. For any…