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A differential approach for bounding the index of graphs under perturbations

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Dalfó Simó, CristinaMés informacióMés informació
Fiol Mora, Miquel ÀngelMés informacióMés informacióMés informació
Garriga Valle, ErnestMés informació
Document typeArticle
Defense date2011-09-02
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
Abstract
This paper presents bounds for the variation of the spectral radius (G) of a graph G after some perturbations or local vertex/edge modifications of G. The perturbations considered here are the connection of a new vertex with, say, g vertices of G, the addition of a pendant edge (the previous case with g = 1) and the addition of an edge. The method proposed here is based on continuous perturbations and the study of their differential inequalities associated. Within rather economical information (namely, the degrees of the vertices involved in the perturbation), the best possible inequalities are obtained. In addition, the cases when equalities are attained are characterized. The asymptotic behavior of the bounds obtained is also discussed.
CitationDalfo, C.; Fiol, M. A.; Garriga, E. A differential approach for bounding the index of graphs under perturbations. "Electronic journal of combinatorics", 02 Setembre 2011, vol. 18, p. 1-13. 
URIhttp://hdl.handle.net/2117/13161
ISSN1077-8926
Publisher versionhttp://www.combinatorics.org/Volume_18/PDF/v18i1p172.pdf
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  • Departament de Matemàtiques - Articles de revista [2.976]
  • COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions - Articles de revista [290]
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