Borderenergetic graphs of order 12

Document Type: Research Paper

Authors

1 Faculty of Science, University of Kragujevac, Serbia.

2 Faculty of Science, University of Kragujevac, Kragujevac, Serbia

Abstract

A graph G of order n is said to be borderenergetic if its energy is equal to 2n-2 and if G differs from the complete graph Kn. The first such graph was discovered in 2001, but their systematic study started only in 2015. Until now, the number of borderenergetic graphs of order n was determined for n

Keywords


1. D. Cvetković, P. Rowlinson, S. Simić, An Introduction to the Theory of Graph
Spectra, Cambridge Univ. Press, Cambridge, 2010.
2. X. Li, Y. Shi, I. Gutman, Graph Energy, Springer, New York, 2012.
3. I. Gutman, O. E. Polansky, Mathematical Concepts in Organic Chemistry,
Springer, Berlin, 1986.

4. B. J. McClelland, Properties of the latent roots of a matrix: The estimation of π-
electron energies, J. Chem. Phys. 54 (1971) 640−643.
5. I. Gutman, Total π-electron energy of benzenoid hydrocarbons, Topics Curr.
Chem. 162 (1992) 29−63.
6. I. Gutman, T. Soldatović, (n,m)-Type approximations for total π-electron energy of
benzenoid hydrocarbons, MATCH Commun. Math. Comput. Chem. 44 (2001)
169−182.
7. I. Gutman, McClelland-type lower bound for total π-electron energy, J. Chem. Soc.
Faraday Trans. 86 (1990) 3373−3375.
8. D. Cvetković, I. Gutman, The computer system GRAPH: A useful tool in chemical
graph theory, J. Comput. Chem. 7 (1986) 640−644.
9. H. B. Walikar, H. S. Ramane, P. R. Hampiholi, On the energy of a graph, in: R.
Balakrishnan, H. M. Mulder, A. Vijayakumar (Eds.), Graph Connections, Allied
Publishers, New Delhi, 1999, pp. 120−123.
10. I. Gutman, Hyperenergetic molecular graphs, J. Serb. Chem. Soc. 64 (1999)
199−205.
11. I. Gutman, Hyperenergetic and hypoenergetic graphs, in: D. Cvetković, I. Gutman
(Eds.), Selected Topics on Applications of Graph Spectra, Math. Inst., Belgrade,
2011, pp. 113−135.
12. V. Nikiforov, Graphs and matrices with maximal energy, J. Math. Anal. Appl. 327
(2007) 735−738.
13. S. Gong, X. Li, G. Xu, I. Gutman, B. Furtula, Borderenergetic graphs, MATCH
Commun. Math. Comput. Chem.74 (2015) 321−332.
14. Y. Hou, I. Gutman, Hyperenergetic line graphs, MATCH Commun. Math. Comput.
Chem. 43 (2001) 29−39.
15. X. Li, M. Wei, S. Gong, A computer search for the borderenergetic graphs of order
10, MATCH Commun. Math. Comput. Chem. 74 (2015) 333−342.
16. B. Deng, X. Li, I. Gutman, More on borderenergetic graphs, Lin. Algebra Appl.
497 (2016) 199−208.
17. Y. Hou, Q. Tao, Borderenergetic threshold graphs, MATCH Commun. Math.
Comput. Chem. 75 (2016) 253−262.
18. Z. Shao, F. Deng, Correcting the number of borderenergetic graphs of order 10,
MATCH Commun. Math. Comput. Chem. 75 (2016) 263−265.
19. X. Li, M. Wei, X. Zhu, Borderenergetic graphs with small maximum or large
minimum degrees, MATCH Commun. Math. Comput. Chem. 77 (2017) 25−36.
20. B. D. McKay, A. Piperno, Practical graph isomorphism II, J. Symb. Comput. 60
(2013) 94−112.