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

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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 $k$ interior vertices of degree at least 3 are obtained.
DOI : 10.1007/s10587-012-0038-1
Classification : 05C35, 05C50
Keywords: first Dirichlet eigenvalue; bicyclic graph; degree sequence 
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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

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