Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/15376
Title: Graphs associated with matrices over finite fields and their endomorphisms in memory of Professor Michael Neumann and Professor Uri Rothblum
Authors: Huang, LP
Huang, Z
Li, CK
Sze, NS 
Keywords: Chromatic number
Endomorphism
Finite field
Graph
Independence number
Matrix
Issue Date: 2014
Publisher: North-Holland
Source: Linear algebra and its applications, 2014, v. 447, p. 2-25 How to cite?
Journal: Linear algebra and its applications 
Abstract: 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 theorem of geometry on Fm×n.
URI: http://hdl.handle.net/10397/15376
ISSN: 0024-3795
EISSN: 1873-1856
DOI: 10.1016/j.laa.2013.12.030
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