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The eccentricity of a vertex is the maximum distance from it to another vertex, and the average eccentricity of a graph is the mean eccentricity of a vertex. In this paper we introduce average edge and average vertex-edge mean eccentricities of a graph. Moreover, relations among these eccentricities for trees are provided as well as formulas for line graphs… (More)

Keywords: Hilbert matrix Cauchy–Hankel matrix Singular value Lower bound Upper bound a b s t r a c t In this study we mainly obtained upper and lower bounds for extreme singular values of an n Â n complex matrix. Moreover, as an application of this, we got bounds for extreme singular values of Hilbert and Cauchy–Hankel matrices as in the forms H ¼ ð1=ði þ j… (More)

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