Geodesic
Tridiagonal matrices and spectral properties of some graph classes
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 1125-1138

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

A graph is called a chain graph if it is bipartite and the neighbourhoods of the vertices in each colour class form a chain with respect to inclusion. In this paper we give an explicit formula for the characteristic polynomial of any chain graph and we show that it can be expressed using the determinant of a particular tridiagonal matrix. Then this fact is applied to show that in a certain interval a chain graph does not have any nonzero eigenvalue. A similar result is provided for threshold graphs.
DOI : 10.21136/CMJ.2020.0182-19
Classification : 05C50
Keywords: tridiagonal matrix; threshold graph; chain graph; eigenvalue-free interval 
@article{10_21136_CMJ_2020_0182_19,
     author = {Andeli\'c, Milica and Du, Zhibin and da Fonseca, Carlos M. and Simi\'c, Slobodan K.},
     title = {Tridiagonal matrices and spectral properties of some graph classes},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1125--1138},
     publisher = {mathdoc},
     volume = {70},
     number = {4},
     year = {2020},
     doi = {10.21136/CMJ.2020.0182-19},
     mrnumber = {4181801},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0182-19/}
}
TY  - JOUR
AU  - Andelić, Milica
AU  - Du, Zhibin
AU  - da Fonseca, Carlos M.
AU  - Simić, Slobodan K.
TI  - Tridiagonal matrices and spectral properties of some graph classes
JO  - Czechoslovak Mathematical Journal
PY  - 2020
SP  - 1125
EP  - 1138
VL  - 70
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0182-19/
DO  - 10.21136/CMJ.2020.0182-19
LA  - en
ID  - 10_21136_CMJ_2020_0182_19
ER  - 
%0 Journal Article
%A Andelić, Milica
%A Du, Zhibin
%A da Fonseca, Carlos M.
%A Simić, Slobodan K.
%T Tridiagonal matrices and spectral properties of some graph classes
%J Czechoslovak Mathematical Journal
%D 2020
%P 1125-1138
%V 70
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0182-19/
%R 10.21136/CMJ.2020.0182-19
%G en
%F 10_21136_CMJ_2020_0182_19
Andelić, Milica; Du, Zhibin; da Fonseca, Carlos M.; Simić, Slobodan K. Tridiagonal matrices and spectral properties of some graph classes. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 1125-1138. doi: 10.21136/CMJ.2020.0182-19

Cité par Sources :