Ruiting Zhang | Searcharxiv

arXiv2023

On the maximal Sombor index of quasi-tree graphs

The Sombor index $SO(G)$ of a graph $G$ is the sum of the edge weights $\sqrt{d^2_G(u)+d^2_G(v)}$ of all edges $uv$ of $G$, where $d_G(u)$ denotes the degree of the vertex $u$ in $G$. A connected graph $G = (V ,E)$ is called a quasi-tree, if there exists $u\in V (G)$ such that $G-u$ is a tree. Denote $\mathscr{Q}(n,k)$=\{$G$: $G$ is a quasi-tree graph of order $n$ with $G-u$ being a tree and $d_G(u)=k$\}. In this paper, we determined the maximum, the second maximum and the third maximum Sombor indices of all quasi-tree graphs in $\mathscr{Q}(n,k)$, respectively. Moreover, we characterized their corresponding extremal graphs, respectively.

math.CO↗

arXiv2021

Learning transferable and discriminative features for unsupervised domain adaptation

Although achieving remarkable progress, it is very difficult to induce a supervised classifier without any labeled data. Unsupervised domain adaptation is able to overcome this challenge by transferring knowledge from a labeled source domain to an unlabeled target domain. Transferability and discriminability are two key criteria for characterizing the superiority of feature representations to enable successful domain adaptation. In this paper, a novel method called \textit{learning TransFerable and Discriminative Features for unsupervised domain adaptation} (TFDF) is proposed to optimize these two objectives simultaneously. On the one hand, distribution alignment is performed to reduce domain discrepancy and learn more transferable representations. Instead of adopting \textit{Maximum Mean Discrepancy} (MMD) which only captures the first-order statistical information to measure distribution discrepancy, we adopt a recently proposed statistic called \textit{Maximum Mean and Covariance Discrepancy} (MMCD), which can not only capture the first-order statistical information but also capture the second-order statistical information in the reproducing kernel Hilbert space (RKHS). On the other hand, we propose to explore both local discriminative information via manifold regularization and global discriminative information via minimizing the proposed \textit{class confusion} objective to learn more discriminative features, respectively. We integrate these two objectives into the \textit{Structural Risk Minimization} (RSM) framework and learn a domain-invariant classifier. Comprehensive experiments are conducted on five real-world datasets and the results verify the effectiveness of the proposed method.

cs.LG↗

arXiv2021

Burning numbers of t-unicyclic graphs

Given a graph $G$, the burning number of $G$ is the smallest integer $k$ for which there are vertices $x_1, x_2,\ldots,x_k$ such that $(x_1,x_2,\ldots,x_k)$ is a burning sequence of $G$. It has been shown that the graph burning problem is NP-complete, even for trees with maximum degree three, or linear forests. A $t$-unicyclic graph is a unicycle graph with exactly one vertex of degree greater than $2$. In this paper, we first present the bounds for the burning number of $t$-unicyclic graphs, and then use the burning numbers of linear forests with at most three components to determine the burning number of all $t$-unicyclic graphs for $t\le 2$.

math.CO↗