Maxima of the Q-index: Degenerate graphs


Let G be a k-degenerate graph of order n. It is well-known that G has no more edges than Sn,k, the join of a complete graph of order k and an independent set of order n-k. In this note, it is shown that Sn,k is extremal for some spectral parameters of G as well. More precisely, letting μ (H) and q (H) denote the largest eigenvalues of the adjacency matrix and the signless Laplacian of a graph H, the inequalities μ(G)<μ(Sn,k) and q(G)

Publication Title

Electronic Journal of Linear Algebra