Some further bounds for the Q-index of nested split graphs

Abstract

The Q-index of a simple graph is the largest eigenvalue of its signless Laplacian, or Q-matrix. In our previous paper [1] we gave three lower and three upper bounds for the Q-index of nested split graphs, also known as threshold graphs. In this paper, we give another two upper bounds, which are expressed as solutions of cubic equations (in contrast to quadratics from [1]). Some computational results are also included.