Abstract:
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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. |