Maynooth University

Maynooth University ePrints and eTheses Archive

Maynooth University Library

Algebraic Connectivity for Vertex-Deleted Subgraphs, and a Notion of Vertex Centrality

Kirkland, Steve (2010) Algebraic Connectivity for Vertex-Deleted Subgraphs, and a Notion of Vertex Centrality. Discrete Mathematics, 310 (4). pp. 911-921. ISSN 0012-365X

[img] Download (207kB)
Official URL: http://www.sciencedirect.com/science?_ob=MImg&_ima...

Abstract

Let G be a connected graph, suppose that v is a vertex of G, and denote the subgraph formed from G by deleting vertex v by G\v. Denote the algebraic connectivities of G and G\v by α(G) and (G\v), respectively. In this paper, we consider the functions ∅(v) = α(G)− α(G\v) and k(v) = α(G\v)/α(G), provide attainable upper and lower bounds on both functions, and characterise the equality cases in those bounds. The function yields a measure of vertex centrality, and we apply that measure to analyse certain graphs arising from food webs.

Item Type: Article
Keywords: Algebraic connectivity; Vertex-deleted subgraph; Vertex centrality; Hamilton Institute.
Subjects: Science & Engineering > Hamilton Institute
Science & Engineering > Mathematics & Statistics
Item ID: 1894
Identification Number: 10.1016/j.disc.2009.10.011
Depositing User: Hamilton Editor
Date Deposited: 23 Mar 2010 10:06
Journal or Publication Title: Discrete Mathematics
Publisher: Elsevier BV, North-Holland
Refereed: Yes
URI:

Repository Staff Only(login required)

View Item Item control page

Document Downloads

More statistics for this item...