The smallest signless Laplacian eigenvalue of graphs under perturbation

Abstract

Abstract. In this paper, we investigate how the smallest signless Laplacian eigenvalue of a graph behaves when the graph is perturbed by deleting a vertex, subdividing edges or moving edges.

On the sign patterns of the smallest signless Laplacian eigenvector

“…Perturbation of µ(G). The recent paper [19] studies how µ(G) is affected by small changes in the structure of G, such as vertex deletion or edge subdivision. Our work can be seen as a counterpart to theirs by examining instead the changes in the corresponding eigenvector -a more daunting problem.…”