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Algebraic connectivity of k-connected graphs

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Abstract

Let G be a k-connected graph with k ⩾ 2. 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).

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Authors and Affiliations

  1. Department of Mathematics, University of Manitoba, 342 Machray Hall, 186 Dysart Road, Winnipeg, MB, R3T 2N2, Canada

    Steve Kirkland

  2. Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Avenida Bento Gonçalves, 9500, Bairro Agronomia, Porto Alegre, CEP 91509-900, Rio Grande do Sul, Brazil

    Israel Rocha & Vilmar Trevisan

Authors
  1. Steve Kirkland
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  2. Israel Rocha
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  3. Vilmar Trevisan
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Correspondence to Steve Kirkland.

Additional information

Steve Kirkland’s research is supported in part by the University of Manitoba under grant 315729-352500-2000. This work is part of the doctoral studies of Israel Rocha, who acknowledges the partial support of CAPES. Vilmar Trevisan is partially supported by CNPq-Grants 305583/2012-3 and 481551/2012-3, by FAPERGS-Grant 11/1619-2, and by CAPES/DAAD Grant PROBRAL 408/13-Brazil.

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Kirkland, S., Rocha, I. & Trevisan, V. Algebraic connectivity of k-connected graphs. Czech Math J 65, 219–236 (2015). https://doi.org/10.1007/s10587-015-0170-9

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  • DOI: https://doi.org/10.1007/s10587-015-0170-9

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