Document Type

Journal Article

Department/Unit

Department of Mathematics

Abstract

A matrix called Varchenko matrix associated with a hyperplane arrangement was defined by Varchenko in 1991. Matrices that we shall call q-matrices are induced from Varchenko matrices. Many researchers are interested in the invariant factors of these q-matrices. In this paper, we associate this problem with a graph theoretic model. We will discuss some general properties and give some methods for finding the invariant factors of q-matrices of certain types of graphs. The proofs are elementary. The invariant factors of complete graphs, complete bipartite graphs, even cycles, some hexagonal systems, and some polygonal trees are found.

Keywords

q-matrix, Invariant factors, Bipartite graph, Hyperplane arrangement

Publication Date

2004

Source Publication Title

Discrete Mathematics

Volume

288

Issue

1-3

Start Page

135

End Page

148

Publisher

Elsevier

Peer Reviewed

1

DOI

10.1016/j.disc.2004.07.009

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.disc.2004.07.009

ISSN (print)

0012365X

Included in

Mathematics Commons

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