AI 中文总结
该研究针对图论中的凯梅尼常数，引入布雷斯团概念，证实存在$\ell\geq3$的布雷斯$K_\ell$，几乎所有连通平面标号图都具备该性质，并探讨了布雷斯边与布雷斯团的关联。
AI 中文摘要
凯梅尼常数被用作图上平均旅行时间的度量。图的布雷斯悖论指：在某些图中添加一条边时，凯梅尼常数会增大。我们引入布雷斯团$K_\ell$的概念，即当将该团插入到含$\ell$个顶点的独立集构成的图中时，会使凯梅尼常数增大的团；在此语境下，布雷斯边即布雷斯$K_2$。我们给出了存在$\ell\geq3$的布雷斯$K_\ell$的图的例子，观察到几乎所有连通平面标号图对每个$\ell\geq3$都存在布雷斯$K_\ell$，还探讨了图中布雷斯边与布雷斯团的关系。
英文摘要
Kemeny's constant is used as a measure of the average travel time on a graph. Braess' paradox for graphs is the observation that in some graphs, when an edge is added, Kemeny's constant increases. We introduce the notion of a Braess clique $K_\ell$, a clique that when inserted into a graph on an independent set of $\ell$ vertices, will create an increase in Kemeny's constant. In this context, a Braess edge is a Braess $K_2$. We provide examples of graphs that have a Braess $K_\ell$ for $\ell\geq 3$. We observe that almost every connected planar labelled graph has a Braess $K_\ell$ for each $\ell\geq 3$. We also explore the relationship between Braess edges and Braess cliques in graphs.
