期刊论文

Sze, Nung-Sing

英文

Linear Algebra and its Applications

0024-3795

2014

447

2-25

10.1016/j.laa.2013.12.030

The research of L.-P. Huang was supported by a National Natural Science Foundation of China (Project 11371072 ) and a Scientific Research Fund of Hunan Provincial Education Department (grant No. 10A002 ). Li and Sze were partially supported by a Hong Kong RGC grant PolyU 502411 ; this grant supported the post-doctoral fellowship of Z. Huang at the Hong Kong Polytechnic University. Li was also supported by a USA NSF grant; he was a visiting professor of the University of Hong Kong in the spring of 2012, an honorary professor of Taiyuan University of Technology (100 Talent Program scholar), and an honorary professor of the Shanghai University. Finally, the authors wish to thank the referee for valuable comments and suggestions and bringing our attention to references [2,14,15,19] .

本校为第一机构

Let Fm×n be the set of m×n matrices over a field F. Consider a graph G=(Fm×n,∼) with Fm×n as the vertex set such that two vertices A,B∈Fm×n are adjacent if rank(A-B)=1. We study graph properties of G when F is a finite field. In particular, G is a regular connected graph with diameter equal to min{m,n}; it is always Hamiltonian. Furthermore, we determine the independence number, chromatic number and clique number of G. These results are used to characterize the graph endomorphisms of G, which extends Hua's fundamental the...