The integral 3-harmonic graphs

AbstractLet G be a graph on n vertices v1,…,vn and let d(vi) be the degree of the vertex vi. If d(G)=(d(v1),…,d(vn))⊤ is an eigenvector of the (0,1)-adjacency matrix A of G, i.e. A(G)d(G)=λd(G), then G is said to be λ-harmonic. In this paper all connected integral 3-harmonic graphs are determined. There are exactly 26 such graphs