arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2111.03330math.CO
收藏

自逆混合图是极其罕见的

Self-converse mixed graphs are extremely rare

Pepijn Wissing

摘要:

关于通常的邻接矩阵,一个混合图与它的逆是共谱的。因此,很容易看出,特征值唯一出现的混合图,直到同构,必须同构于它的逆。因此,人们自然会问,这是否是一种普遍现象。本文从理论上证明了自逆混合图的分数趋于零。

英文摘要:

A mixed graph is cospectral to its converse, with respect to the usual adjacency matrices. Hence, it is easy to see that a mixed graph whose eigenvalues occur uniquely, up to isomorphism, must be isomorphic to its converse. It is therefore natural to ask whether or not this is a common phenomenon. This note contains the theoretical evidence to confirm that the fraction of self-converse mixed graphs tends to zero.

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。

↑