Invariant factors of graphs associated with hyperplane arrangements

Wai Chee SHIU*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

4 Citations (Scopus)
17 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)135-148
Number of pages14
JournalDiscrete Mathematics
Issue number1-3
Publication statusPublished - 28 Nov 2004

Scopus Subject Areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

User-Defined Keywords

  • Bipartite graph
  • Hyperplane arrangement
  • Invariant factors
  • Q-matrix


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