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In this paper, we present some inequalities for the Co-PI index involving the some topological indices, the number of vertices and edges, and the maximum degree. After that, we give a result for trees. In addition, we give some inequalities for the largest eigenvalue of the Co-PI matrix of G.

- Kinkar Chandra Das, Ismail Naci Cangul, Ayse Dilek Maden, Ahmet Sinan Cevik
- 2013

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 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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