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

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• 作者：Ayse Dilek Maden (1)
  Ahmet Sinan Cevik (1)
  Ismail Naci Cangul (2)
  Kinkar C Das (3)
  
• 关键词：Kirchhoff matrix ; Kirchhoff Estrada index ; Kirchhoff energy ; lower and upper bounds
• 刊名：Journal of Inequalities and Applications
• 出版年：2013
• 出版时间：December 2013
• 年：2013
• 卷：2013
• 期：1
• 全文大小：210KB
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• 作者单位：Ayse Dilek Maden (1)
  Ahmet Sinan Cevik (1)
  Ismail Naci Cangul (2)
  Kinkar C Das (3)
  
  1. Department of Mathematics, Faculty of Science, Sel莽uk University, Campus, Konya, 42075, Turkey
  2. Department of Mathematics, Faculty of Arts and Science, Uludag University, Gorukle Campus, Bursa, 16059, Turkey
  3. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, Republic of Korea
  
• ISSN：1029-242X

文摘

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. MSC: 05C12, 05C50, 05C90.