Algebraic connectivity of $k$-connected graphs

Czechoslovak Mathematical Journal

Steve Kirkland¹  Israel Rocha² 

[1] Department of Mathematics, University of Manitoba, 342 Machray Hall, 186 Dysart Road, Winnipeg, MB R3T 2N2, Canada;Vilmar Trevisan, Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Avenida Bento Gonalves, 9500, Bairro Agronomia, Porto Alegre, CEP 91509-900, Rio Grande do Sul, Brazil

关键词: algebraic connectivity;    Fiedler vector;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

Let $G$ be a $k$-connected graph with $k \ge2$. A hinge is a subset of $k$ vertices whose deletion {}from $G$ yields a disconnected graph. We consider the algebraic connectivity and Fiedler vectors of such graphs, paying special attention to the signs of the entries in Fielder vectors corresponding to vertices in a hinge, and to vertices in the connected components at a hinge. The results extend those in Fiedler's papers Algebraic connectivity of graphs (1973), A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory (1975), and Kirkland and Fallat's paper Perron Components and Algebraic Connectivity for Weighted Graphs (1998).

【 授权许可】

Unknown