Title :
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
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;
Conference_Titel :
Control Conference (CCC), 2012 31st Chinese
Conference_Location :
Hefei
Print_ISBN :
978-1-4673-2581-3
