13 papers
On the generalized cospectral mates of chain graphs of rank 4
Wei Wang, Siqi Wu
A graph is called a chain graph if it is bipartite and the neighborhoods of the vertices in each color class are linearly ordered by inclusion. We study the generalized spectral de…
Nearly permanental cospectral graphs
Weifang Lv, Quanyu Tang, Wei Wang +1
Let be a simple graph of order with adjacency matrix . The \emph{determinant} and the \emph{permanen}t of the matrix are defined as \[\mathrm{det}A= \sum_{…
A Family of Simultaneously Cospectral Trees for Degree-Distance Matrices
Limeng Lin, Quanyu Tang, Kehua Wang +1
Spectral characterization of graphs for various graph matrices constitutes a central topic in spectral graph theory. Let be a graph with adjacency matrix , diagonal degre…
Generalized spectral closedness of -free graph classes
Wei Wang, Quanyu Tang
In this paper, we investigate the generalized spectral closedness of graph classes defined by a family of forbidden induced subgraphs. To systematically study this pr…
Orthogonal degree-similarity of edge-deleted strongly regular graphs
Yi-Zheng Fan, Wei Wang, Kuo Zhang
Godsil and Sun asked whether, for a strongly regular graph and any two different edges and , the edge-deleted graphs and are degree-similar…
Smith normal forms for coalescences at cospectral vertices
Yi-Zheng Fan, Kuo Zhang, Wei Wang
Let be the generalized -adjacency matrix of a finite graph . Fan, Xing, Zhang, and Wang constructed pairs of non-degree-similar trees for which the Smith…
Factorization of invariant polynomials and generalized spectral characterizations of graphs
Wei Wang, Quanyu Tang
The problem of characterizing graphs by their generalized spectra has received significant attention in recent years. This paper provides a complete proof of a conjecture proposed…
On a generalization of the Johnson-Newman theorem to multiple rank-one perturbations
Wei Wang, Siqi Wu
Wang and Zhao (Adv. Appl. Math. 173 (2026) 102994) generalized the classic Johnson-Newman theorem on simultaneous similarity of symmetric matrices from a single rank-one perturbati…
A very short note on a problem of Godsil and Sun
Wei Wang
Using the spectral theorem for symmetric matrices over a real closed field, we give a quick answer to a problem of Godsil and Sun on degree-similarity of graphs.
On the common index jump theorem and further developments
Huagui Duan, Yiming Long, Wei Wang +1
In [LZ02] published in Annals of Mathematics, Long and Zhu established originally the common index jump theorem (CIJT) for symplectic paths in 2002, which has played an important r…
Degree-similar graphs and cospectral graphs
Yi-Zheng Fan, Ruo-Jie Xing, Yi-Liu Zhang +1
Let be a graph with adjacency matrix and degree matrix , and let . Two graphs and are called \emph{degree-similar} if there exists…
New arithmetic invariants for cospectral graphs
Yizhe Ji, Quanyu Tang, Wei Wang +1
An invariant for cospectral graphs is a property shared by all cospectral graphs. In this paper, we establish three novel arithmetic invariants for cospectral graphs, revealing dee…
On the Positive and Negative -Energies of Graphs under Edge Addition
Quanyu Tang, Yinchen Liu, Wei Wang
In this paper, we introduce the concepts of positive and negative -energies of graphs and investigate their behavior under edge addition. Specifically, we generalize the classic…