The spectral radius of graphs with no intersecting odd cycles

Abstract

Let Hs,t1,…,tk be the graph with s triangles and k odd cycles of lengths t1,…,tk≥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 Hs,t1,…,tk 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,t1,…,tk for n large enough.