The k - Domination number and bounds for the Laplacian eigenvalues of graphs

Abstract

Two results on the bounds for the algebraic connectivity and the largest Laplacian eigenvalue of a graph were presented by Lu, Liu, and Tian in [5] (Bounds of Laplacian spectrum of graphs based on the domination number, Linear Algebra and its Applications 402 (2005) 390-396). It is attempted in this note to generalize the two results of Lu, Liu, and Tian.