You are here

Home » Content

Randi ́c Energy and Randi ́c Estrada Index of a Graph

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2012

Key Words:

Author NameUniversity of AuthorFaculty of Author

AMS Codes:

Abstract (2. Language): 
Let G be a simple connected graph with n vertices and let di be the degree of its i-th vertex. The Randi´c matrix of G is the square matrix of order n whose ! i, j " -entry is equal to 1/ # didj if the i-th and j-th vertex of G are adjacent, and zero otherwise. The Randi´c eigenvalues are the eigenvalues of the Randi´c matrix. The Randi´c energy is the sum of the absolute values of the Randi´c eigenvalues. In this paper, we introduce a new index of the graph G which is called Randi´c Estrada index. In addition, we obtain lower and upper bounds for the Randi´c energy and the Randi´c Estrada index of G.
Bookmark/Search this post with
FULL TEXT (PDF): 
PDF icon arastirmax-randi-c-energy-and-randi-c-estrada-index-graph.pdf
  • 1
88-99
  • English

REFERENCES

References: 

[1] ¸S Bozkurt, A Güngör, I Gut man and A Çevi k. Randi ´c Matrix and Randi´c Energy. MATCH
Commun. Math. Comput. Chem. 64. 239-250. 2010.
[2] ¸S Bozkurt, A Güngör, andI Gut man. Randi ´c Spectral Radius and Randi´c Energy. MATCH
Commun. Math. Comput. Chem. 64. 321-334. 2010.
[3] D Cvetkovi´c, M Doob and H Sachs. Spectra of Graphs-Theory and Application (Third ed.
Johann Ambrosius Bart Verlag, Heidelberg, Leipzig). 1995.
[4] K Das and S Lee. On the Estrada index conjecture. Linear Algebra Appl. 431. 1351-1359.
2009.
[5] J De la Peña, I Gutman and J Rada. Estimating the Estrada index. Linear Algebra Appl.
427. 70-76. 2007.
[6] H Deng, S Radenkovi´c and I Gutman. The Estrada index in: D. Cvetkovic, I. Gutman
(Eds.) Applications of Graph Spectra (Math. Inst., Belgrade). 123-140. 2009.
[7] E Estrada. Characterization of 3D molecular structure. Chem. Phys. Lett. 319. 713-718.
2000.
[8] E Estrada. Characterization of the folding degree of proteins. Bioinformatics 18. 697-
704. 2002.
[9] E Estrada and J Rodríguez-Velázguez. Subgraph centrality in complex networks. Phys.
Rev. E 71. 056103-056103-9.2005.
[10] E Estrada, J Rodríguez-Velázguez adn M Randi´c. Atomic Branching in molecules. Int.
J.Quantum Chem. 106. 823-832. 2006.
[11] I Gutman. Bounds for total $-electron energy. Chem. Phys. Lett. 24. 283-285. 1974.
[12] I Gutman. Total $-electron energy of benezoid hydrocarbons. Topics Curr. Chem. 162.
26-63. 1992.
[13] I Gutman. The energy of a graph, old and new results, in: A. Betten, A. Kohnert,
R. Laue, A. Wassermann (Eds.), Algebraic Combinatorics and Applications (Springer-
Verlag, Berlin) 196-211. 2001.
[14] J Liu and B Liu. Bounds of the Estrada index of graphs. Appl. Math. J. Chinese Univ. 25
(3). 325-330. 2010.
[15] M Randi´c. On characterization of moleculer branching, J. A. Chem. Soc. 97. 6609-6615.
1975.

Thank you for copying data from http://www.arastirmax.com