On the Kirchhoff matrix, a new Kirchhoff index and the Kirchhoff energy

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Date

2013

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Volume Title

Publisher

Springer

Abstract

The main purpose of this paper is to define and investigate the Kirchhoff matrix, a new Kirchhoff index, the Kirchhoff energy and the Kirchhoff Estrada index of a graph. In addition, we establish upper and lower bounds for these new indexes and energy. In the final section, we point out a new possible application area for graphs by considering this new Kirchhoff matrix. Since graph theoretical studies (including graph parameters) consist of some fixed point techniques, they have been applied in the fields such as chemistry (in the meaning of atoms, molecules, energy etc.) and engineering (in the meaning of signal processing etc.), game theory, and physics.

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Keywords

Mathematics, Kirchhoff matrix, Kirchhoff Estrada index, Kirchhoff energy, Lower and upper bounds, Resistance distance, Complex network, Folding degree, Extrada index

Citation

Maden, A. D. vd. (2013). “On the Kirchhoff matrix, a new Kirchhoff index and the Kirchhoff energy”. Journal of Inequalities and Applications, 2013.