A differential approach for bounding the index of graphs under perturbations

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Title:	A differential approach for bounding the index of graphs under perturbations
Author:	Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
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.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs -Graph algorithms -Adjacency matrix -Spectral radius -Grafs, Teoria de -Classificació AMS::05 Combinatorics::05C Graph theory
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Document type:	Article - Published version Article
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