Geodesic
Partial characterization of graphs having a single large Laplacian eigenvalue
L. Emilio Allem1 ; Antonio Cafure2 ; Ezequiel Dratman3 ; Luciano N. Grippo3 ; Martín D. Safe4 ; Vilmar Trevisan1
1Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Brazil
2Instituto del Desarrollo Humano, Universidad Nacional de General Sarmiento, Argentina Depto. de Matemática, CBC, Universidad de Buenos Aires, Argentina
3Instituto de Ciencia. Universidad Nacional de General Sarmiento. Argentina.
4Departamento de Matemática, Universidad Nacional del Sur, Argentina.
The electronic journal of combinatorics, Tome 25 (2018) no. 4
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

The parameter $\sigma(G)$ of a graph $G$ stands for the number of Laplacian eigenvalues greater than or equal to the average degree of $G$. In this work, we address the problem of characterizing those graphs $G$ having $\sigma(G)=1$. Our conjecture is that these graphs are stars plus a (possible empty) set of isolated vertices. We establish a link between $\sigma(G)$ and the number of anticomponents of $G$. As a by-product, we present some results which support the conjecture, by restricting our analysis to cographs, forests, and split graphs.
DOI : 10.37236/7342
Classification : 05C50
Mots-clés : Laplacian matrix, Laplacian eigenvalues

L. Emilio Allem  1   ; Antonio Cafure  2   ; Ezequiel Dratman  3   ; Luciano N. Grippo  3   ; Martín D. Safe  4   ; Vilmar Trevisan  1

1 Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Brazil
2 Instituto del Desarrollo Humano, Universidad Nacional de General Sarmiento, Argentina Depto. de Matemática, CBC, Universidad de Buenos Aires, Argentina
3 Instituto de Ciencia. Universidad Nacional de General Sarmiento. Argentina.
4 Departamento de Matemática, Universidad Nacional del Sur, Argentina. 
@article{10_37236_7342,
     author = {L. Emilio Allem and Antonio Cafure and Ezequiel Dratman and Luciano N. Grippo and Mart{\'\i}n D. Safe and Vilmar Trevisan},
     title = {Partial characterization of graphs having a single large {Laplacian} eigenvalue},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {4},
     doi = {10.37236/7342},
     zbl = {1406.05061},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7342/}
}
TY  - JOUR
AU  - L. Emilio Allem
AU  - Antonio Cafure
AU  - Ezequiel Dratman
AU  - Luciano N. Grippo
AU  - Martín D. Safe
AU  - Vilmar Trevisan
TI  - Partial characterization of graphs having a single large Laplacian eigenvalue
JO  - The electronic journal of combinatorics
PY  - 2018
VL  - 25
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.37236/7342/
DO  - 10.37236/7342
ID  - 10_37236_7342
ER  - 
%0 Journal Article
%A L. Emilio Allem
%A Antonio Cafure
%A Ezequiel Dratman
%A Luciano N. Grippo
%A Martín D. Safe
%A Vilmar Trevisan
%T Partial characterization of graphs having a single large Laplacian eigenvalue
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/7342/
%R 10.37236/7342
%F 10_37236_7342
L. Emilio Allem; Antonio Cafure; Ezequiel Dratman; Luciano N. Grippo; Martín D. Safe; Vilmar Trevisan. Partial characterization of graphs having a single large Laplacian eigenvalue. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/7342

Cité par Sources :