Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599702 | Linear Algebra and its Applications | 2014 | 24 Pages |
Abstract
Let FmÃn be the set of mÃn matrices over a field F. Consider a graph G=(FmÃn,â¼) with FmÃn as the vertex set such that two vertices A,BâFmÃn are adjacent if rank(AâB)=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 theorem of geometry on FmÃn.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Li-Ping Huang, Zejun Huang, Chi-Kwong Li, Nung-Sing Sze,