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.

Publication Year

2004

Journal Title

Discrete Mathematics

Volume number

288

Issue number

1-3

Publisher

Elsevier

First Page (page number)

135

Last Page (page number)

148

Referreed

1

DOI

10.1016/j.disc.2004.07.009

ISSN (print)

1872681X

Keywords

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

Included in

Mathematics Commons

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