Lower bound for the second smallest eigenvalue of directed rooted graph Laplacian

Author

Chao, Huang ; Xudong, Ye

Author_Institution

Coll. of Electr. Eng., Zhejiang Univ., Hangzhou, China

fYear

2012

fDate

25-27 July 2012

Firstpage

5994

Lastpage

5997

Abstract

A lower bound for the second smallest eigenvalue (SSE) of the unweighted Laplacian for an N-vertex directed rooted graph is obtained by obtaining the supremum of the scrambling constant of the (N-1)-th power of the corresponding adjacency matrix. This supremum is actually achieved by the ”N-layer Complete Graph” (NCG) defined in this paper, which implies that for directed rooted graphs that is unweighted for its directed edges, NCGs have the least connective topology in the sense of scrambling constant.

Keywords

Laplace equations; directed graphs; eigenvalues and eigenfunctions; matrix algebra; multi-robot systems; N-layer complete graph; N-vertex directed rooted graph; SSE; adjacency matrix; directed edge; directed rooted graph Laplacian; least connective topology; multiagent system; scrambling constant supremum; second smallest eigenvalue; unweighted Laplacian; Educational institutions; Eigenvalues and eigenfunctions; Graph theory; Laplace equations; Markov processes; Network topology; Topology; Algebraic connectivity; Graph Laplacian; Multi-agent systems; Scrambling constant; Second smallest eigenvalue;

fLanguage

English

Publisher

ieee

Conference_Titel

Control Conference (CCC), 2012 31st Chinese

Conference_Location

Hefei

ISSN

1934-1768

Print_ISBN

978-1-4673-2581-3

Type

conf

Filename

6390992