Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-05-21 , DOI: 10.1080/03081087.2020.1766405 Ji-Hwan Jung 1 , Suh-Ryung Kim 1, 2 , Bumtle Kang 2 , Gi-Sang Cheon 2, 3
ABSTRACT
Given disjoint non-empty subsets S and T of , a digraph D with the vertex set is called a directed Toeplitz graph provided the arc occurs if and only if or . We investigate strong connectivity and primitivity of directed Toeplitz graphs. We prove that any primitive directed Toeplitz graph with vertices has exponent at least 3 and for each , there is a primitive directed Toeplitz graph of order n which has exponent 3. By Wielandt's result, we know that for a primitive digraph D of order n. We characterize the primitive directed Toeplitz graph, for which the upper bound it attained.
中文翻译:
原始有向 Toeplitz 图的指数
摘要
给定不相交的非空子集S和T, 一个有向图D与顶点集被称为有向 Toeplitz 图,前提是弧当且仅当发生或者. 我们研究有向 Toeplitz 图的强连通性和原始性。我们证明了任何原始的有向 Toeplitz 图顶点的指数至少为 3 并且对于每个,有一个原始的n阶有向 Toeplitz 图,其指数为 3。根据 Wielandt 的结果,我们知道对于n阶的原始有向图D。我们描述了原始有向 Toeplitz 图,它达到了上限。