具有正则图的有限格的一些注记

Some Remarks on Regular Graph Lattices

研究了一类具有正则图的有限格,称之为正则图格.证明了一个有限格是分配的正则图格当且仅当它是布尔格,同时找出了所有1阶和2阶的正则图格.特别地,证明了8-元素布尔格是最小的3阶正则图格.

A regular graph lattice is a lattice whose Hass diagram is a regular graph.It is shown that a finite distributive lattice is a regular graph lattice if and only if it is a Boolean lattice.All the 1-degree graph lattices and 2-degree graph lattices are found.It is shown that the 8-element Boolean lattice is the smallest 3-degree regular graph lattice.