6 papers
On the Tutte polynomial of series-parallel posets
Jianxuan Luo, Tingzeng Wu, Hong-Jian Lai
The Tutte polynomial is a bivariate polynomial that has been extensively studied in graph and matroid theory. Gordon was the first to study the Tutte polynomial of the g…
Hook immanantal equalities for linear combination matrices of (di)graphs and their applications
Xiangshuai Dong, Tingzeng Wu, HongJian Lai
Let be an irreducible character of the symmetric group . For an matrix , define the immanant of corresponding to by \begin{eqnarray*…
Realizing degree sequences with -connected graphs
Rui Guan, Chenglin Jiang, Hong-Jian Lai +2
A graph is -connected if, for any mapping with , there exists a strongly connected orientati…
On the edge reconstruction of the second immanantal polynomials of undirected graph and digraph
Tingzeng Wu, Yafan Geng, Hong-Jian Lai
Let be an matrix. The second immanant of matrix 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…
Improved bounds for the coefficient of flow polynomials
Tingzeng Wu, Shuang Ma, Hong-Jian Lai
Let be a connected bridgeless -graph which may have loops and multiedges, and let denote the flow polynomial of . Dong and Koh \cite{Dong1} established an up…
Solution to an open problem on Laplacian ratio
T. Wu
Let G be a graph. The Laplacian ratio of G is the permanent of the Laplacian matrix of G divided by the product of degrees of all vertices. The computational complexity of Laplacia…