1. The first Dirichlet eigenvalue of bicyclic graphs
- Creator:
- Zhang, Guang-Jun and Zhang, Xiao-Dong
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- first Dirichlet eigenvalue, bicyclic graph, and degree sequence
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public