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Spectral Characterization of Families of Split Graphs

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Abstract

An upper bound for the sum of the squares of the entries of the principal eigenvector corresponding to a vertex subset inducing a k-regular subgraph is introduced and applied to the determination of an upper bound on the order of such induced subgraphs. Furthermore, for some connected graphs we establish a lower bound for the sum of squares of the entries of the principal eigenvector corresponding to the vertices of an independent set. Moreover, a spectral characterization of families of split graphs, involving its index and the entries of the principal eigenvector corresponding to the vertices of the maximum independent set is given. In particular, the complete split graph case is highlighted.

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Authors and Affiliations

  1. Department of Mathematics, Center for Research and Development in Mathematics and Applications, University of Aveiro, 3810-193, Aveiro, Portugal

    Milica Anđelić & Domingos M. Cardoso

  2. Faculty of Mathematics, University of Belgrade, Belgrade, Serbia

    Milica Anđelić

Authors
  1. Milica Anđelić
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  2. Domingos M. Cardoso
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Corresponding author

Correspondence to Domingos M. Cardoso.

Additional information

Research supported in part by FEDER funds through COMPETE—Operational Programme Factors of Competitiveness (“Programa Operacional Factores de Competitividade”) and by Portuguese funds through the Center for Research and Development in Mathematics and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (“FCT - Fundação para a Ciência e a Tecnologia”), within project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690. The work of first author was supported by Serbian Ministry of Science, Project 174033.

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Anđelić, M., Cardoso, D.M. Spectral Characterization of Families of Split Graphs. Graphs and Combinatorics 31, 59–72 (2015). https://doi.org/10.1007/s00373-013-1387-8

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  • DOI: https://doi.org/10.1007/s00373-013-1387-8

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