4 papers · 1 filter
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 …
On a conjecture of Nikiforov concerning the minimal -energy of connected graphs
Quanyu Tang, Yinchen Liu, Wei Wang
For a given simple graph \( G \), the \( p \)-energy of \( G \), denoted by \( \mathcal{E}_p(G) \), is defined as the sum of the \( p \)-th power of the absolute values of the eige…
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…