论距离保持图和序列距离保持图
On Distance Preserving and Sequentially Distance Preserving Graphs
AI总结：
该研究针对距离保持图和序列距离保持图，基于单纯形排序给出序列距离保持的等价条件，证明无≥5阶导出圈的图是序列距离保持图，还研究了含割点图的相关性质并定义了非距离保持图族。
摘要：
若图$H$是图$G$的子图且对任意$u,v∈V(H)$满足$d_H(u,v)=d_G(u,v)$，则$H$是$G$的等距子图。距离保持图指其包含所有可能阶数的等距子图；序列距离保持图指顶点可排序，使得删除前$i$个顶点后仍为等距子图（对所有$i≥1$）。我们基于单纯形排序给出序列距离保持的等价条件，证明不含长度≥5的导出圈的图是序列距离保持图（因此也是距离保持图），还研究了含割点图的距离保持性质，最后定义了由圈构造的非距离保持图族。
英文摘要：
A graph $H$ is an \emph{isometric} subgraph of $G$ if $d_H(u,v)= d_G(u,v)$, for every pair~$u,v\in V(H)$. A graph is \emph{distance preserving} if it has an isometric subgraph of every possible order. A graph is \emph{sequentially distance preserving} if its vertices can be ordered such that deleting the first $i$ vertices results in an isometric subgraph, for all $i\ge1$. We give an equivalent condition to sequentially distance preserving based upon simplicial orderings. Using this condition, we prove that if a graph does not contain any induced cycles of length~$5$ or greater, then it is sequentially distance preserving and thus distance preserving. Next we consider the distance preserving property on graphs with a cut vertex. Finally, we define a family of non-distance preserving graphs constructed from cycles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
