A characterization of graphs with rank 4

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

Research output: Contribution to journalArticlepeer-review

72 Scopus citations


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 with rank 4? This question has not yet been fully answered in the literature, and only some partial results are known. In this paper we resolve this question by completely characterizing graphs G whose adjacency matrix has rank 4.

Original languageEnglish
Pages (from-to)1793-1798
Number of pages6
JournalLinear Algebra and Its Applications
Issue number8
StatePublished - 15 Apr 2011


  • Adjacency matrix
  • Graph
  • Nullity
  • Rank
  • Spectrum


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