Ayse Dilek Maden

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For p, q, r, s, t ∈ Z + with rt ≤ p and st ≤ q, let G = G(p, q; r, s; t) be the bipartite graph with partite sets U = {u v q } such that any two edges u i and v j are not adjacent if and only if there exists a positive integer k with 1 ≤ k ≤ t such that (k – 1)r + 1 ≤ i ≤ kr and (k – 1)s + 1 ≤ j ≤ ks. Under these circumstances, Chen et al. presented the(More)
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  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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