Energy of graphs

Document Type : Survey

Author

Department of pure math, University of Kashan

Abstract

The energy, E(G), of a simple graph G is defined to be the sum of the absolute values of the eigen values of G. In this paper, we introduce some in-equalities of energy of graphs.

Graphical Abstract

Energy of graphs

Keywords


[1] N. Abreu, D .M. Cardoso, I. Gutman, E. A. Martins, M. Robbiano, Bounds for the signless Laplacian energy, Lin. Algebra Appl. 435 (2011) 2365–2374.
[2] C. Adiga, R. Balakrishnan, W. So, The skew energy of digraph, Lin. Algebra Appl. 432 (2010)
1825–1835.
[3] C. Adiga, M. Smitha, On the skew Laplacian energy of a digraph, Int, Math. Forum 4 (2009) 1907–1914.
[4] C. Adiga, M. Smitha, On maximum degree energy of a graph, Int. J. Contemp. Math. Sci. 4 (2009) 385–396.
[5] A. Alwardi, N. D. Soner, I. Gutman, On the common neighborhood energy of a graph, Bull. Acad, Serbe Sci. Arts (CI. Math. Natur.) 143 (2011) 49–59.
[6] S. K. Ayyaswamy, S. Balachandran, I. Gutman, On second-stage spectrum and energy of a graph, Kragujevac J. Math. 34 (2010) 135–146.
[7] S. B. Bozkurt, A. D. Gungor, I. Gutman, Note on distance energy of graphs, MATCH, Commun.
Math. Comput. Chem. 64 (2010) 129–134.
[8] S. B. Bozkurt, A. D. G Yung Yor, I. Gutman, A. S Cevik, Randic matrix and Randic energy, MATCH
Commun. Math. Comput. Chem, 64 (2010) 239–250.
[9] Z. Cui, B. Liu, On Harary matrix, Harary energy, MATCH Commun. Math. Comput. Chem. 68 (2012) 815–823.
[10] D. Cvetkovi´c, P. Rowlinson, S. Simi´c, An introduction to the Theory of Graph Spectra, Cambridge Univ. Press, Cambridge, 2010.
[11] A. D. Gung Yor, A. S. Cevik, On the Harary energy and Harary Estrada index of a graph, MATCH
Commun. Math. Comput. Chem. 64 (2010) 281–296.
[12] I. Gutman, The energy of a graph, Ber. Math Statist. Sekt. Forschungsz. Graz. 103 (1978) 1–22.
[13] I. Gutman, B. Furtula, Survey of graph energies, Math. Interdisc. Res. 2 (2017) 85–129.
[14] I. Gutman, B. Zhou, Laplacian energy of a graph, Lin. Algebra Appl. 414 (2006) 29–37.
[15] M. Ghorbani, M. Songhori, Polyhedral graphs via their automorphism groups, Appl. Math. Comput. 321 (2018) 1–10.
[16] M. Jalali-Rad, Eigenvalues, energy of the Cayley graph of some groups with respect to a normal subset, Math. Interdisc. Res. 2 (2017) 193–207.
[17] G. James, M. Liebeck, Representations and Characters of Groups, Cambridge Univ. Press,
London-New York, 1993.
[18] V. Nikiforov, The energy of graphs and matrices, J. Math. Anal. Appl. 326 (2007) 1472–1475.
[19] F. Nowroozi-Larki, M. Ghorbani, On the spectrum of Cayley graphs via character table, J. Math. Nanosci. 4 (2011) 1–11.
Volume 8, Issue 3
September 2023
Pages 229-234
  • Receive Date: 24 October 2022
  • Revise Date: 02 November 2022
  • Accept Date: 16 November 2022
  • Publish Date: 01 September 2023