Sharp bounds on the signless laplacian spectral radii of graphs

The signless Laplacian spectral radii of modified graphs

In this paper, various modifications of a connected graph G are regarded as perturbations of its signless Laplacian matrix. Several results concerning the resulting changes to the signless Laplacian spectral radius of G are obtained by solving intermediate eigenvalue problems of the second type. AMS subject classifications: 05C50

Ordering of the signless Laplacian spectral radii of unicyclic graphs

For n ≥ 11, we determine all the unicyclic graphs on n vertices whose signless Laplacian spectral radius is at least n− 2. There are exactly sixteen such graphs and they are ordered according to their signless Laplacian spectral radii.

Sharp bounds for the signless Laplacian spectral radius of digraphs

Sharp Bounds on the PI Spectral Radius

In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.

The (signless) Laplacian spectral radii of c-cyclic graphs with n vertices and k pendant vertices

A connected graph is called a c-cyclic graph if it contains n vertices and n + c − 1 edges. Let C(n, k, c) denote the class of connected c-cyclic graphs with n vertices and k pendant vertices. Recently, the unique extremal graph, which has greatest (respectively, signless) Laplacian spectral radius, in C(n, k, c) has been determined for 0 ≤ c ≤ 3, k ≥ 1 and n ≥ 2c + k + 1. In this paper, the un...