Sharp spectral bounds for complex perturbations of the indefinite Laplacian

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.

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 pimatrices of a graph g are obtained. those graphs for which these bounds are best possible arecharacterized.

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 upper bounds for the Laplacian graph eigenvalues

Let G = (V ,E) be a simple connected graph and λ1(G) be the largest Laplacian eigenvalue of G. In this paper, we prove that: 1. λ1(G) = max{du +mu : u ∈ V } if and only if G is a regular bipartite or a semiregular bipartite graph, where du and mu denote the degree of u and the average of the degrees of the vertices adjacent to u, respectively. 2. λ1(G) = 2 + √ (r − 2)(s − 2) if and only if G is...