sharp bounds on the pi spectral radius

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.

Some Sharp Upper Bounds on the Spectral Radius of Graphs

In this paper, we first give a relation between the adjacency spectral radius and the Q-spectral radius of a graph. Then using this result, we further give some new sharp upper bounds on the adjacency spectral radius of a graph in terms of degrees and the average 2-degrees of vertices. Some known results are also obtained.

Sharp bounds for the signless Laplacian spectral radius of digraphs

Sharp Bounds on the Spectral Radius and the Energy of Graphs

Abstract Let G = (V,E) be a simple graph of order n with V (G) = {v1, v2, . . . , vn} and degree sequence d1, d2, . . . , dn. Let ρ(G) be the largest eigenvalue of adjacency matrix of G, and let E(G) be the energy of G. Denote (t)i = ∑ i∼j d α j and (m)i = (t)i/di , where α is a real number. In this paper, we obtain two sharp bounds on ρ(G) in terms of (m)i or (t)i, respectively. Also, we prese...

Sharp Upper Bounds on the Spectral Radius of the Laplacian Matrix of Graphs

Let G = (V,E) be a simple connected graph with n vertices and e edges. Assume that the vertices are ordered such that d1 ≥ d2 ≥ . . . ≥ dn, where di is the degree of vi for i = 1, 2, . . . , n and the average of the degrees of the vertices adjacent to vi is denoted by mi. Let mmax be the maximum of mi’s for i = 1, 2, . . . , n. Also, let ρ(G) denote the largest eigenvalue of the adjacency matri...

Sharp bounds on the spectral radius of nonnegative matrices and digraphs

Article history: Received 03 May 2012 Accepted 26 April 2013 Available online 24 May 2013 Submitted by R.A. Brualdi