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

Maden A. D., ÇEVİK A. S., CANGÜL İ. N., Das K. C.

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2013
  • Doi Number: 10.1186/1029-242x-2013-337
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Kirchhoff matrix, Kirchhoff Estrada index, Kirchhoff energy, lower and upper bounds, RESISTANCE DISTANCE, COMPLEX NETWORKS, FOLDING DEGREE, ESTRADA INDEX
  • Bursa Uludag University Affiliated: Yes


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.