The first Dirichlet eigenvalue of bicyclic graphs
Guang-Jun Zhang, Xiao-Dong Zhang (2012)
Czechoslovak Mathematical Journal
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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 interior vertices...