A characterization of graphs with rank 5

Gerard J. Chang, Liang Hao Huang, Hong Gwa Yeh

Research output: Contribution to journalArticlepeer-review

53 Scopus citations

Abstract

The rank of a graph G is defined to be the rank of its adjacency matrix. In this paper,we consider the following problem: what is the structure of a connected graph G with rank 5? or equivalently, what is the structure of a connected n-vertex graph G whose adjacency matrix has nullity n - 5? In this paper, we completely characterize connected graphs G whose adjacency matrix has rank 5.

Original languageEnglish
Pages (from-to)4241-4250
Number of pages10
JournalLinear Algebra and Its Applications
Volume436
Issue number11
DOIs
StatePublished - 1 Jun 2012

Keywords

  • Adjacency matrix
  • Graph
  • Nullity
  • Rank
  • Spectrum

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