The set of graph eigenvalues of the adjacency matrix is called the spectrum of the graph. (But note that in physics, the eigenvalues of the Laplacian matrix of a graph are sometimes known as the graph's spectrum.) The spectrum of a graph G with n_i-fold degenerate eigenvalues λ_i is commonly denoted Spec(G) = (λ_1)^(n_1) (λ_2)^(n_2) ... or (λ_1 | λ_2 | ... n_1 | n_2 | ...). The product product_k(x - s_k) over the elements of the spectrum of a graph G is known as the characteristic polynomial of G, and is given by the characteristic polynomial of the adjacency matrix of G with respect to the variable x.

algebraic connectivity | characteristic polynomial | cospectral graphs | determined by spectrum | graph eigenvalue | integral graph | Laplacian matrix | spectral radius