Normalized algebraic connectivity of graphs

Abstract

Let [Formula: see text] be the second smallest normalized Laplacian eigenvalue of a graph [Formula: see text], called the normalized algebraic connectivity of [Formula: see text]. In this paper, we study the relation between the normalized algebraic connectivity of the coalescence of two graphs and that of these two graphs. Furthermore, we investigate how the normalized algebraic connectivity behaves when the graph is perturbed by relocating pendent edges.