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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
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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; Vertex-deleted 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, North-Holland |
| Refereed: | Yes |
| Related URLs: | |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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