Kirkland, Steve (2010) Algebraic Connectivity for VertexDeleted Subgraphs, and a Notion of Vertex Centrality. Discrete Mathematics, 310 (4). pp. 911921. ISSN 0012365X
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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; Vertexdeleted subgraph; Vertex centrality; Hamilton Institute. 
Academic Unit:  Faculty of Science and Engineering > Research Institutes > Hamilton Institute Faculty of Science and Engineering > Mathematics and 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, NorthHolland 
Refereed:  Yes 
URI: 
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