The first Dirichlet eigenvalue of bicyclic graphs
Guang-Jun Zhang; Xiao-Dong Zhang
Czechoslovak Mathematical Journal (2012)
- Volume: 62, Issue: 2, page 441-451
- ISSN: 0011-4642
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topZhang, Guang-Jun, and Zhang, Xiao-Dong. "The first Dirichlet eigenvalue of bicyclic graphs." Czechoslovak Mathematical Journal 62.2 (2012): 441-451. <http://eudml.org/doc/246212>.
@article{Zhang2012,
abstract = {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.},
author = {Zhang, Guang-Jun, Zhang, Xiao-Dong},
journal = {Czechoslovak Mathematical Journal},
keywords = {first Dirichlet eigenvalue; bicyclic graph; degree sequence; first Dirichlet eigenvalue; bicyclic graph; degree sequence},
language = {eng},
number = {2},
pages = {441-451},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The first Dirichlet eigenvalue of bicyclic graphs},
url = {http://eudml.org/doc/246212},
volume = {62},
year = {2012},
}
TY - JOUR
AU - Zhang, Guang-Jun
AU - Zhang, Xiao-Dong
TI - The first Dirichlet eigenvalue of bicyclic graphs
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 2
SP - 441
EP - 451
AB - 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.
LA - eng
KW - first Dirichlet eigenvalue; bicyclic graph; degree sequence; first Dirichlet eigenvalue; bicyclic graph; degree sequence
UR - http://eudml.org/doc/246212
ER -
References
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