Variances and determinantal profiles of orientations

Huilan Chang*, Sen Peng Eu, Pei Lan Yen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Given a simple graph G, let X be the random variable which is the determinant of the (oriented) adjacency matrix of an orientation of G. It is known that the expectation E(X) equals the number of perfect matchings of G. In this paper we give a graphical interpretation of the variance Var(X). We also give complete determinantal profiles of several classes of graphs, including wheels, fans, and general books.

Original languageEnglish
Pages (from-to)209-223
Number of pages15
JournalLinear Algebra and Its Applications
Publication statusPublished - 2014 Sept 15


  • Determinant
  • Orientation
  • Pfaffian
  • Variance

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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