Topic:The cyclic index of adjacency tensor of generalized power hypergraphs
Speaker: Professor Fan Yizheng
Event date: 1/16/2019
Event time: 16:10 p.m.
Venue: Lecture Hall 204, Building 9
Sponsor: School of Mathematics and Statistics, Institute of Science and Technology
Abstract: Let $G$ be a $t$-uniform hypergraph, and let $c(G)$ denote the cyclic index of the adjacency tensor of $G$. Let $m,s,t$ be positive integers such that $t \ge 2$,$s \ge 2$ and $m=st$. The generalized power $G^{m,s}$ of $G$ is obtained from $G$ by blowing up each vertex into an $s$-set and preserving the adjacencyrelation. It was conjectured that $c(G^{m,s})=s \cdot c(G)$. In this paper we show that the conjecture is false by giving a counter example, and give some sufficient conditions for the conjecture holding. Finally we give an equivalent characterization of the equality in the conjecture by using a matrix equation over $\mathbb{Z}_m$.