The first Dirichlet eigenvalue of bicyclic graphs
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 441-451.

Voir la notice de l'article dans Czech Digital Mathematics Library

In this paper, we have investigated some properties of the first Dirichlet eigenvalue of a bicyclic graph with boundary condition. These results can be used to characterize the extremal bicyclic graphs with the smallest first Dirichlet eigenvalue among all the bicyclic graphs with a given graphic bicyclic degree sequence with minor conditions. Moreover, the extremal bicyclic graphs with the smallest first Dirichlet eigenvalue among all the bicycle graphs with fixed $k$ interior vertices of degree at least 3 are obtained.
DOI : 10.1007/s10587-012-0038-1
Classification : 05C35, 05C50
Mots-clés : first Dirichlet eigenvalue; bicyclic graph; degree sequence 
@article{10_1007_s10587_012_0038_1,
     author = {Zhang, Guang-Jun and Zhang, Xiao-Dong},
     title = {The first {Dirichlet} eigenvalue of bicyclic graphs},
     journal = {Czechoslovak Mathematical Journal},
     pages = {441--451},
     publisher = {mathdoc},
     volume = {62},
     number = {2},
     year = {2012},
     doi = {10.1007/s10587-012-0038-1},
     mrnumber = {2990185},
     zbl = {1265.05429},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0038-1/}
}
TY  - JOUR
AU  - Zhang, Guang-Jun
AU  - Zhang, Xiao-Dong
TI  - The first Dirichlet eigenvalue of bicyclic graphs
JO  - Czechoslovak Mathematical Journal
PY  - 2012
SP  - 441
EP  - 451
VL  - 62
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0038-1/
DO  - 10.1007/s10587-012-0038-1
LA  - en
ID  - 10_1007_s10587_012_0038_1
ER  - 
%0 Journal Article
%A Zhang, Guang-Jun
%A Zhang, Xiao-Dong
%T The first Dirichlet eigenvalue of bicyclic graphs
%J Czechoslovak Mathematical Journal
%D 2012
%P 441-451
%V 62
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0038-1/
%R 10.1007/s10587-012-0038-1
%G en
%F 10_1007_s10587_012_0038_1
Zhang, Guang-Jun; Zhang, Xiao-Dong. The first Dirichlet eigenvalue of bicyclic graphs. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 441-451. doi : 10.1007/s10587-012-0038-1. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0038-1/

Cité par Sources :