图的内幂及其坚韧度

Abstract

图的直积运算具有许多很好的结构性质，其中之一是满足消去律，即:对任意 两个图G和H以及正整数k，Gk∼=Hk当且仅当G∼=H，这里Gk表示G的直积 k次幂。Hammack和Liversay定义了图的一种新的乘积运算，称为图的k次内幂运 算，并希望该运算也具有消去律，但随后他们很快注意到这一结论当k是偶数时是 不正确的。尽管如此，他们猜想当k是奇数时结论是成立的。 从定义不难看出图的内幂运算非常类似于图的直积运算。因此，除了消去律， 研究者还研究了内幂运算的其它结构性质，如连通性、二部性、哈密尔顿性等。 坚韧度(toughness)是Chvatal&acut...

The direct product of graphs has many nice structural properties, one of which is the so-called cancellation law, that is, for any two graphs G and H, Gk ∼= Hk if and only if G ∼= H. Hammack and Liversay introduced a new product operation of graphs, namely the k-th inner power, and hope that it has similar cancellation law. Unfortunately, almost at the same time, they found that th...