Some problems in Hermitian energies of mixed graphs

: 15h00, ngày 24/06/2022 (Thứ Sáu)

: P104 D3

: Seminar Toán rời rạc

: Ngô Quốc Hoàn

: Viện Toán ứng dụng và Tin học, ĐH Bách Khoa Hà Nội

Tóm tắt báo cáo

The Hermitian adjacency matrix of a mixed graph $G = (V, E)$ of order $n$ is the $n \times n$ matrix $H(G) = (a_{ij})$ that is defined by
\begin{eqnarray}
a_{ij} &=& \left\lbrace \begin{matrix}
i & \mbox{ if } (v_i, v_j) \in E\\
-i & \mbox{ if } (v_j, v_i) \in E\\
1 &\mbox{ if } \left( (v_i, v_j) \in E \mbox{ and } (v_j, v_i) \in E\right) \\
0 & \mbox{ otherwise. }
\end{matrix} \right.
\end{eqnarray}
for any $i, j = 1, \ldots , n$.
On addition, the energy of a mixed graph $G$ (which is also called the Hermitian energy of $G$), namely by $\mathcal{E}_H(G)$, is the sum of absolute values of eigenvalues of $H(G)$.
This talk presents some important results of the energy of a mixed graph $G$ and some properties of the spectrum of the Hermitian adjacency matrix of a mixed graph $G$.


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