On graphs whose second largest eigenvalue does not exceed (√5−1)2

AbstractIt is well known in the theory of graph spectra that connected graphs except for complete multipartite (including complete) graphs have the second largest eigenvalue greater than 0. Graphs whose second largest eigenvalue does not exceed 13 are characterized in Cao and Yuan (1993). In this paper we study the structure of graphs whose second largest eigenvalue does not exceed (√5−1)2