7 papers · 1 filter
A New Sufficient Condition for Oriented Graphs Determined by Their Generalized Skew Spectra
Limeng Lin, Wei Wang, Hao Zhang
Characterizing graphs uniquely determined by their spectra (DS) is a core open problem in spectral graph theory. While this problem has been extensively investigated for simple und…
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_{…
An Upper Bound on the Number of Generalized Cospectral Mates of Oriented Graphs
Limeng Lin, Wei Wang, Hao Zhang
This paper examines the spectral characterizations of oriented graphs. Let be an -vertex oriented graph with skew-adjacency matrix . Previous research mainly focused on s…
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…
The Generation of All Regular Rational Orthogonal Matrices
Quanyu Tang, Wei Wang, Hao Zhang
A \emph{rational orthogonal matrix} is an orthogonal matrix with rational entries, and is called \emph{regular} if each of its row sum equals one, i.e., where …
Annihilating polynomial, Jordan canonical from, and generalized spectral characterizations of Eulerian graphs
Kunyue Li, Wei Wang, Hao Zhang
Let be an Eulerian graph on vertices with adjacency matrix and characteristic polynomial . We show that when is even (resp. odd), the square-root of (r…
A new criterion for oriented graphs to be determined by their generalized skew spectrum
Yiquan Chao, Wei Wang, Hao Zhang
Spectral characterizations of graphs is an important topic in spectral graph theory which has been studied extensively by researchers in recent years. The study of oriented graphs,…