关于一致超图直积的循环指数

On cyclic index of direct product of uniform hypergraphs

设G和H为m-一致超图,G×H为G和H的直积.研究直积G×H的循环指数c(G×H)和因子超图的循环指数c(G),c(H)之间的联系,证明了G×H是谱[c(G),c(H)]-对称的,从而[c(G),c(H)]整除c(G×H),其中[a,b]记正整数a,b的最小公倍数.

Let G and H be two m-uniform hypergraphs,and let G×H be the direct product of G and H.This paper studied the relationship between the cyclic index c(G×H)of the product G×H and the cyclic indexes c(G),c(H)of the its factors,and proved that G×H was spectral[c(G),c(H)]-symmetric,and hence[c(G),c(H)]divides c(G×H),where[a,b]denoted the least common multiple of integers a,b.