两类Cayley图的Hamilton性

Hamiltonian Property of Two Class of Cayley Graphs

域Ｆ上的所有ｍ×ｎ矩阵记为Ｆ（ｍ×ｎ），域Ｆ上的所有ｎ×ｎ可逆矩阵构成的乘群，称为一般线性群，记为ＧＬｎ（Ｆ），当Ｆ是无限可列数域时，本文证明了Ｆ（ｍ×ｎ）和ＧＬｎ（Ｆ）上的连通Ｃａｙｌｅｙ图是无限连通的，从而可Ｈａｍｉｌｔｏｎ分解．

This paper conside two class of Cayley graphs of all m×n matrixes F(m×n) on the general linear groups GLn (F) over infinitely countable number field. Following results are obtained:(i) The Cayley. graphs on F(m×n) or GLn (F) are infinitely connected.(ii) The Cayley graphs on F(m×n) or CLn (F) can be decomposed into any combination of one-way and two-way infinite Hamiltonian paths.