On the rank of a cograph

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

doi:10.1016/j.laa.2008.03.016

On the rank of a cograph

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

The rank of a graph is defined to be the rank of its adjacency matrix. Royle [G.F. Royle, The rank of a cograph, Electron. J. Combin. 10 (2003) #N11] proved a somewhat surprising result that the rank of a cograph is equal to the number of distinct non-zero rows of its adjacency matrix. In this paper we answer a question posed by Royle (2003) by giving an elementary short proof for a more general setting of this rank property of cographs.

Original language	English
Pages (from-to)	601-605
Number of pages	5
Journal	Linear Algebra and Its Applications
Volume	429
Issue number	2-3
DOIs	https://doi.org/10.1016/j.laa.2008.03.016
State	Published - 15 Jul 2008

Keywords

Cograph
Complement reducible graph
Decomposable graph
Join
Rank
Twins
Union

Access to Document

10.1016/j.laa.2008.03.016

Cite this

@article{028b1085a8a84fd5b2cb04e2b1c9c03d,

title = "On the rank of a cograph",

abstract = "The rank of a graph is defined to be the rank of its adjacency matrix. Royle [G.F. Royle, The rank of a cograph, Electron. J. Combin. 10 (2003) #N11] proved a somewhat surprising result that the rank of a cograph is equal to the number of distinct non-zero rows of its adjacency matrix. In this paper we answer a question posed by Royle (2003) by giving an elementary short proof for a more general setting of this rank property of cographs.",

keywords = "Cograph, Complement reducible graph, Decomposable graph, Join, Rank, Twins, Union",

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

note = "Funding Information: E-mail addresses: [email protected] (G.J. Chang), [email protected] (L.-H. Huang), hgyeh@math. ncu.edu.tw (H.-G. Yeh). 1 Partially supported by National Science Council of ROC under Grant NSC95-2115-M-002-013-MY3. 2 Partially supported by National Science Council of ROC under Grant NSC95-2115-M-008-005.",

year = "2008",

month = jul,

day = "15",

doi = "10.1016/j.laa.2008.03.016",

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

volume = "429",

pages = "601--605",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

number = "2-3",

}

TY - JOUR

T1 - On the rank of a cograph

AU - Chang, Gerard J.

AU - Huang, Liang Hao

AU - Yeh, Hong Gwa

N1 - Funding Information: E-mail addresses: [email protected] (G.J. Chang), [email protected] (L.-H. Huang), hgyeh@math. ncu.edu.tw (H.-G. Yeh). 1 Partially supported by National Science Council of ROC under Grant NSC95-2115-M-002-013-MY3. 2 Partially supported by National Science Council of ROC under Grant NSC95-2115-M-008-005.

PY - 2008/7/15

Y1 - 2008/7/15

N2 - The rank of a graph is defined to be the rank of its adjacency matrix. Royle [G.F. Royle, The rank of a cograph, Electron. J. Combin. 10 (2003) #N11] proved a somewhat surprising result that the rank of a cograph is equal to the number of distinct non-zero rows of its adjacency matrix. In this paper we answer a question posed by Royle (2003) by giving an elementary short proof for a more general setting of this rank property of cographs.

AB - The rank of a graph is defined to be the rank of its adjacency matrix. Royle [G.F. Royle, The rank of a cograph, Electron. J. Combin. 10 (2003) #N11] proved a somewhat surprising result that the rank of a cograph is equal to the number of distinct non-zero rows of its adjacency matrix. In this paper we answer a question posed by Royle (2003) by giving an elementary short proof for a more general setting of this rank property of cographs.

KW - Cograph

KW - Complement reducible graph

KW - Decomposable graph

KW - Join

KW - Rank

KW - Twins

KW - Union

UR - http://www.scopus.com/inward/record.url?scp=43749119588&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2008.03.016

DO - 10.1016/j.laa.2008.03.016

M3 - 期刊論文

AN - SCOPUS:43749119588

SN - 0024-3795

VL - 429

SP - 601

EP - 605

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 2-3

ER -

On the rank of a cograph

Abstract

Keywords

Access to Document

Fingerprint

Cite this