## On the spectral radius of bicyclic graphs.(English)Zbl 1120.05310

The authors determine the graph with maximal spectral radius among connected bicyclic graphs of order $$n$$, possessing $$k$$ pendent vertices. This is the graph having two triangles with a common vertex at which $$k$$ paths of almost equal length are attached. In fact, this paper finishes previous research on the topic since in the paper by the third author [Linear Algebra Appl. 408, 75–85 (2005; Zbl 1073.05550)] the problem of finding extremal graphs was reduced to just two candidates.

### MSC:

 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)

graph spectra

Zbl 1073.05550
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