Hong-Jian Lai

collaborators

4 papers

math.CO2025

Hook immanantal equalities for linear combination matrices of (di)graphs and their applications

Xiangshuai Dong, Tingzeng Wu, HongJian Lai

Let $χ_{λ}$ be an irreducible character of the symmetric group $S_{n}$ . For an $n \times n$ matrix $M = (m_{ij})$ , define the immanant of $M$ corresponding to $χ_{λ}$ by \begin{eqnarray*…

math.CO2025

Realizing degree sequences with $S_{3}$ -connected graphs

Rui Guan, Chenglin Jiang, Hong-Jian Lai +2

A graph $G$ is $S_{3}$ -connected if, for any mapping $β : V (G) \mapsto Z_{3}$ with $\sum_{v \in V (G)} β (v) \equiv 0 (mod 3)$ , there exists a strongly connected orientati…

math.CO2025

On the edge reconstruction of the second immanantal polynomials of undirected graph and digraph

Tingzeng Wu, Yafan Geng, Hong-Jian Lai

Let $M = (m_{ij})$ be an $n \times n$ matrix. The second immanant of matrix $M$ is defined by \begin{eqnarray*} d_{2}(M)=\sum_{σ\in S_{n}}χ_{2}(σ)\prod_{s=1}^{n}m_{sσ(s)}, \end{eqnarr…

math.CO2025

Improved bounds for the coefficient of flow polynomials

Tingzeng Wu, Shuang Ma, Hong-Jian Lai

Let $G$ be a connected bridgeless $(n, m)$ -graph which may have loops and multiedges, and let $F (G, t)$ denote the flow polynomial of $G$ . Dong and Koh \cite{Dong1} established an up…

Hook immanantal equalities for linear combination matrices of (di)graphs and their applications

Realizing degree sequences with S3​-connected graphs

On the edge reconstruction of the second immanantal polynomials of undirected graph and digraph

Improved bounds for the coefficient of flow polynomials

Realizing degree sequences with $S_{3}$ -connected graphs