A differential approach for bounding the index of graphs under perturbations
This paper presents bounds for the variation of the spectralradiusλ(G) ofa graphGafter some perturbations or local vertex/edge modifications ofG. Theperturbations considered here are the connection of a new vertex with, say,gverticesofG, the addition of a pendant edge (the previous case withg= 1) an...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10459.1/463240 |
| Acceso en línea: | https://doi.org/10.37236/659 https://hdl.handle.net/10459.1/463240 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph Adjacency matrix Spectral radius Graph perturbation Dif-ferential inequalities |
| Sumario: | This paper presents bounds for the variation of the spectralradiusλ(G) ofa graphGafter some perturbations or local vertex/edge modifications ofG. Theperturbations considered here are the connection of a new vertex with, say,gverticesofG, the addition of a pendant edge (the previous case withg= 1) and the additionof an edge. The method proposed here is based on continuous perturbations andthe study of their differential inequalities associated. Within rather economicalinformation (namely, the degrees of the vertices involved in the perturbation), thebest possible inequalities are obtained. In addition, the cases when equalities areattained are characterized. The asymptotic behavior of thebounds obtained isalso discussed. For instance, ifGis a connected graph andGudenotes the graphobtained fromGby adding a pendant edge at vertexuwith degreeδu, then,λ(Gu)≤λ(G) +δuλ3(G)+ o(1λ3(G)) |
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