$n$ -立方体的局部三角图和正规子
Locally triangular graphs and normal quotients of the $n$-cube
摘要：
对于整数$n\geq 2$，三角图的顶点集是$\{1,\ldots,n\}$的$2$ -子集，边集是相交于一点的$2$ -子集对.这样的图被称为二分矩形图的二等分图，二分矩形图是连通的无三角形图，其中每个$2$ -路位于唯一的四边形中。我们改进了这一结果，并提供了一个特征的连通局部三角形图的正常的双叉图的$n$ -立方体。要做到这一点，我们研究了一个参数，推广的概念，最小距离的二进制线性码的任意自同构群的$n$立方体。
英文摘要：
For an integer $n\geq 2$, the triangular graph has vertex set the $2$-subsets of $\{1,\ldots,n\}$ and edge set the pairs of $2$-subsets intersecting at one point. Such graphs are known to be halved graphs of bipartite rectagraphs, which are connected triangle-free graphs in which every $2$-path lies in a unique quadrangle. We refine this result and provide a characterisation of connected locally triangular graphs as halved graphs of normal quotients of $n$-cubes. To do so, we study a parameter that generalises the concept of minimum distance for a binary linear code to arbitrary automorphism groups of the $n$-cube.
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。
