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oai:recercat.cat:2117/131612025-07-17T01:03:37Zcom_2072_1033col_2072_452950

A differential approach for bounding the index of graphs under perturbations Dalfó Simó, Cristina Fiol Mora, Miquel Àngel Garriga Valle, Ernest Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions 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 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. Postprint (published version) 2011-09-02 Article Dalfo, 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. 1077-8926 https://hdl.handle.net/2117/13161 eng http://www.combinatorics.org/Volume_18/PDF/v18i1p172.pdf Open Access 13 p. application/pdf