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.


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


graph spectra


Zbl 1073.05550
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