Note on laplacian energy of graphs

Bulletin, Classe des Sciences Mathematiques et Naturelles, Sciences Mathematiques

Volumn 137, Issue 33, 2008, Pages 1-10

  Fath Tabar, G H ^a,b   Ashrafi, A R ^a,b   Gutman, I ^a,b  

^a UNIVERSITY OF KASHAN   (Iran)

^b UNIVERSITY OF KRAGUJEVAC   (Serbia)

Author keywords

Laplacian energy (of graph); Laplacian spectrum (of graph)

Indexed keywords

EID: 77953900358     PISSN: 05617332     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. D.Cvetković, M. Doob, H. Sachs, Spectra of Graphs - Theory and Application, Barth, Heidelberg, 1995.
2. N.M. M.de Abreu, C. T. M. Vinagre, A. S. Bonifácio, I. Gutman, The Laplacian energy of some Laplacian integral graphs, MATCH Commun. Math. Comput. Chem. 60 (2008), 447-460.
3. M. Fiedler, Algebraic connectivity of graphs, Czech. Math. J. 23 (1973), 298-305.
4. I. Gutman, The energy of a graph, Ber. Math.-Statist. Sekt. Forschungsz. Graz. 103 (1978), 1-22.
5. 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, 2001, pp. 196-211.
6. I. Gutman, Topology and stability of conjugated hydrocarbons. The dependence of total π-electron energy on molecular topology, J. Serb. Chem. Soc. 70 (2005), 441-456.
7. I. Gutman, K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004), 83-92.
8. I. Gutman, N. M. M. deAbreu, C. T. M. Vinagre, A. S. Bonifácio, S. Radenković, Relation between energy and Laplacian energy, MATCH Commun. Math. Comput. Chem. 59 (2008), 343-354.
9. I. Gutman, O. E. Polansky, Mathematical Concepts in Organic Chemistry, Springer-Verlag, Berlin, 1986, chapter 8.
10. I. Gutman, B. Zhou, Laplacian energy of a graph, Lin. Algebra Appl. 414 (2006), 29-37.
11. A. K. Kel'mans, The number of trees in a graph I, Automat. Remote Control 26 (1965), 2118-2129.
12. A. K. Kel'mans, The number of trees in a graph II, Automat. Remote Control 27 (1966), 233-241.
13. A. K. Kel'mans, Properties of the characteristic polynomial of a graph, Kibernetiky na sluzhbu komunizmu 4 (1967) 27-41 (in Russian).
14. J. Liu, B. Liu, A Laplacian-energy-like invariant of a graph, MATCH Commun. Math. Comput. Chem. 59 (2008), 355-372.
15. R. Merris, Laplacian matrices of graphs: A survey, Lin. Algebra Appl. 197-198 (1994), 143-176.
16. R. Merris, A survey of graph Laplacians, Lin. Multilin. Algebra 39 (1995), 19-31.
17. B. Mohar, The Laplacian spectrum of graphs, in: Y. Alavi, G. Chartrand, O. R. Oellermann, A. J. Schwenk (Eds.), Graph Theory, Combinatorics, and Applications, Wiley, New York, 1991, pp. 871-898.
18. S. Nikolić, G. Kovačević, A. Miličević, N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), 113-124.
19. B. Zhou, Zagreb indices, MATCH Commun. Math. Comput. Chem. 52 (2004), 113-118.
20. B. Zhou, I. Gutman, On Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. 57 (2007), 211-220.
21. B. Zhou, I. Gutman, Nordhaus-Gaddum-type relations for the energy and Laplacian energy of graphs, Bull. Acad. Serbe Sci. Arts (Cl. Math. Natur.) 134 (2007), 1-11.