The spectral radius of graphs with no intersecting odd cycles

Let Hs,k be the graph defined by intersecting s triangles and k cycles of odd lengths at least five in exactly one common vertex. Recently, Hou, Qiu and Liu [Discrete Math. 341 (2018) 126–137], and Yuan [J. Graph Theory 89 (2018), no. 1, 26–39] determined independently the maximum number of edges in an n-vertex graph that does not contain Hs,k as a subgraph. In this paper, we determine the graphs of order n that attain the maximum spectral radius among all graphs containing no Hs,k for n large enough.

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