On the second largest distance eigenvalue

The second largest eigenvalue of trees

On the second largest eigenvalue of a mixed graph

Let G be a mixed graph. We discuss the relation between the second largest eigenvalue λ2(G) and the second largest degree d2(G), and present a sufficient condition for λ2(G) ≥ d2(G).

Graphs with small second largest Laplacian eigenvalue

Let L(G) be the Laplacian matrix of G. In this paper, we characterize all of the connected graphs with second largest Laplacian eigenvalue no more than l; where l . = 3.2470 is the largest root of the equation μ3 − 5μ2 + 6μ − 1 = 0. Moreover, this result is used to characterize all connected graphs with second largest Laplacian eigenvalue no more than three. © 2013 Elsevier Ltd. All rights rese...

On the Second Least Distance Eigenvalue of a Graph

Let G be a connected graph on n vertices, and let D(G) be the distance matrix of G. Let ∂1(G) ≥ ∂2(G) ≥ · · · ≥ ∂n(G) denote the eigenvalues of D(G). In this paper, the connected graphs with ∂n−1(G) at least the smallest root of x3 − 3x2 − 11x− 6 = 0 are determined. Additionally, some non-isomorphic distance cospectral graphs are given.

On the Mean of the Second Largest Eigenvalue on the Convergence Rate of Genetic Algorithms

Genetic algorithms are sometimes disparagingly denoted as just a fancier form of a plain, stupid heuristic. One of the main reasons for this kind of critique is that users believed a GA could not guarantee global convergence in a certain amount of time. Because the proof of global convergence of GAs using elitism has been performed elsewhere (11), in this work we want to extend previous work by...