On generalized θθ-graphs whose second largest eigenvalue does not exceed 1

A generalized θθ-graph, denoted by θnθn, is a graph consisting of nn internal disjoint (uu, vv)-paths, where 2≤n<∞2≤n<∞. In this paper, all generalized θθ-graphs whose second largest eigenvalues do not exceed 1 have been determined.