The spectral radius of graphs with no intersecting odd cycles.

Let H s , t 1 , ... , t k be the graph with s triangles and k odd cycles of lengths t 1 , ... , t k ≥ 5 intersecting in exactly one common vertex. Recently, Hou et al. (2018) [27] , and Yuan (2018) [42] determined independently the maximum number of edges in an n -vertex graph that does not contain H s , t 1 , ... , t 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 H s , t 1 , ... , t k for n large enough. [ABSTRACT FROM AUTHOR]