The characterization of graphs with eigenvalue -1 of multiplicity n-4 or n-5

Yuhong Yang, Qiongxiang Huang
2019 Filomat  
Petrović in [M. Petrović, On graphs with exactly one eigenvalue less than −1, J. Combin. Theory Ser. B 52 (1991) 102-112] determined all connected graphs with exactly one eigenvalue less than −1 and all minimal graphs with exactly two eigenvalues less than −1. By using these minimal graphs, in this paper, we determine all connected graphs having −1 as an eigenvalue with multiplicity n − 4 or n − 5.
doi:10.2298/fil1918919y fatcat:uunjvfyp6vf4higxzgi55arl64