根图广义同谱性的刻画及其在图重构中的应用

由块相似矩阵产生的图的保同谱合并集

Coalescing sets preserving cospectrality of graphs arising from block similarity matrices

本文研究图的合并操作何时保持同谱性，通过相似矩阵的块结构给出充分条件，并覆盖邻接、拉普拉斯、无符号拉普拉斯、距离及广义距离矩阵等类型。

On Hosoya's dormants and sprouts

In a recent series of papers, Hosoya drew the attention to a particular aspect of constructing cospectral graphs by using coalescences: that cospectral graphs can be constructed by attaching multiple copies of a rooted graph in different ways to subsets of vertices of an underlying graph. Our principal focus is to address the expectations and questions raised in Hosoya's papers with regards to this construction. We give an explicit formula for the characteristic polynomial of such multiple coalescences, from which we obtain a necessary and sufficient condition for their cospectrality. We enume…

Kelly引理在图重构中用于计数有根子图的精细化

A refinement of Kelly's lemma for graph reconstruction for counting rooted subgraphs

本文精细化Kelly引理，研究计数根顶点与删除顶点重合的有根子图，证明一般不可能，但半径大于k时可计数固定高度k的多重集，并推广至边重构。

毛毛虫tanglegram的重构

Reconstruction of caterpillar tanglegrams

本文研究tanglegram的重构问题，证明当两棵有根二叉树中至少有一棵为caterpillar tree时，大小为$n$的tanglegram可由删除一对匹配叶子导出的大小为$(n-1)$的tanglegram多重集唯一编码。

Generalized Fitch Graphs: Edge-labeled Graphs that are explained by Edge-labeled Trees

Fitch graphs $G=(X,E)$ are di-graphs that are explained by $\{\otimes,1\}$-edge-labeled rooted trees with leaf set $X$: there is an arc $xy\in E$ if and only if the unique path in $T$ that connects the least common ancestor $\textrm{lca}(x,y)$ of $x$ and $y$ with $y$ contains at least one edge with label $1$. In practice, Fitch graphs represent xenology relations, i.e., pairs of genes $x$ and $y$ for which a horizontal gene transfer happened along the path from $\textrm{lca}(x,y)$ to $y$. In this contribution, we generalize the concept of xenology and Fitch graphs and consider complete di-grap…

用图let重建图及其连通性

Reconstructing graphs and their connectivity using graphlets

本文提出利用图let度分布（gdd）重建图及其连通性，证明特定条件下图可被gdd唯一确定，并探讨gdd与图连通性的关系。