@article{93783fa9ee1e446f96a86514b5f0504c,

title = "A characterization of graphs with rank 4",

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 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.",

keywords = "Adjacency matrix, Graph, Nullity, Rank, Spectrum",

author = "Chang, {Gerard J.} and Huang, {Liang Hao} and Yeh, {Hong Gwa}",

note = "Funding Information: Corresponding author. E-mail addresses: gjchang@math.ntu.edu.tw (G.J. Chang), r90221003@gmail.com (L.-H. Huang), hgyeh@math.ncu.edu.tw (H.-G. Yeh). 1 Partially supported by National Science Council under grant NSC98-2115-M-002-013-MY3. 2 Partially supported by National Science Council under grant NSC99-2811-M-008-059. 3 Partially supported by National Science Council under grant NSC97-2628-M-008-018-MY3.",

year = "2011",

month = apr,

day = "15",

doi = "10.1016/j.laa.2010.09.040",

language = "???core.languages.en_GB???",

volume = "434",

pages = "1793--1798",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

number = "8",

}