The Sharpness of a Lower Bound on the Algebraic Connectivity for Maximal Graphs

Authors

Stephen J. Kirkland, University of Regina
Jason J. Molitierno, Sacred Heart UniversityFollow
Michael Neumann, University of Connecticut - Storrs

Document Type

Peer-Reviewed Article

Publication Date

2001

Abstract

Let G be an undirected unweighted graph on n vertices and let L be its Laplacian matrix. It is known that if is the group inverse of L, then for is a lower bound on the algebraic connectivity μ(G of G Merris has introduced and characterized the class of all maximal graphs of all orders. These are graphs whose degree sequence is not majorized by the degree sequence of any other graph. Here we show that if Ç is a maximal graph and L is its Laplacian, then 1/(L #)=μ(Ç). We provide an example to show that the converse of this result is not valid.

Comments

At the time of publication Jason Molitierno was affiliated with University of Connecticut.

DOI

10.1080/03081080108818670

Recommended Citation

Kirkland, S. J., Molitierno, J., & Neumann, M. (2001). The sharpness of a lower bound on the algebraic connectivity for maximal graphs. Linear and Multilinear Algebra, 48(3), 237–246. Doi: 10.1080/03081080108818670