On distance spectral radius and distance energy of graphs

Match

Volumn 64, Issue 1, 2010, Pages 261-280

  Zhou, Bo ^a   Ilić, Aleksandar ^b  

^a SOUTH CHINA NORMAL UNIVERSITY   (China)

^b UNIVERSITY OF NI   (Serbia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77956572755     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (36)

1. D. M. Cvetković, M. Doob, H. Sachs, Spectra of Graphs - Theory and Application, Academic Press, New York, 1980.
2. F. Buckley, F. Harary, Distance in Graphs, Addison-Wesley, Redwood, 1990.
3. A. T. Balaban, D. Ciubotariu, M. Medeleanu, Topological indices and real number vertex invariants based on graph eigenvalues or eigenvectors, J. Chem. Inf. Comput. Sci. 31 (1991) 517-523.
4. I. Gutman, M. Medeleanu, On the structure-dependence of the largest eigenvalue of the distance matrix of an alkane, Indian J. Chem. A37 (1998) 569-573. (Pubitemid 128522917)
5. B. Zhou, On the largest eigenvalue of the distance matrix of a tree, MATCH Commun. Math. Comput. Chem. 58 (2007) 657-662.
6. B. Zhou, N. Trinajstić, On the largest eigenvalue of the distance matrix of a connected graph, Chem. Phys. Lett. 447 (2007) 384-387. (Pubitemid 47562406)
7. B. Zhou, N. Trinajstić, Further results on the largest eigenvalues of the distance matrix and some distance-based matrices of connected (molecular) graphs, Internet Electron. J. Mol. Des. 6 (2007) 375-384.
8. B. Zhou, N. Trinajstić, Mathematical properties of molecular descriptors based on distances, Croat. Chem. Acta, in press.
9. K. C. Das, On the largest eigenvalue of the distance matrix of a bipartite graph, MATCH Commun. Math. Comput. Chem. 62 (2009) 667-672.
10. R. L. Graham, H. O. Pollack, On the addressing problem for loop switching, Bell System Tech. J. 50 (1971) 2495-2519.
11. R. L. Graham, L. Lovász, Distance matrix polynomials of trees, Adv. Math. 29 (1978) 60-88.
12. R. Subhi, D. Powers, The distance spectrum of the path Pπ and the first distance eigenvector of connected graphs, Linear Multilin. Algebra 28 (1990) 75-81.
13. R. Merris, The distance spectrum of a tree, J. Graph Theory 14 (1990) 365-369.
14. D. Stevanovic, A. Ilić, Distance spectral radius of trees with fixed maximum degree, Electron. J. Linear Algebra (2009) submitted.
15. G. Indulal, I. Gutman, A. Vijaykumar, On the distance energy of a graph, MATCH Commun. Math. Comput. Chem. 60 (2008) 461-472.
16. H. S. Ramane, D. S. Revankar, I. Gutman, S. B. Rao, B. D. Acharya, H. B. Walikar, Bounds for the distance energy of a graph, Kragujevac J. Math. 31 (2008) 59-68.
17. G. Indulal, Sharp bounds on the distance spectral radius and the distance energy of graphs, Linear Algebra Appl. 430 (2009) 106-113.
18. H. S. Ramane, D. S. Revankar, I. Gutman, S. B. Rao, B. D. Acharya, H. B. Walikar, Estimating the distance energy of graphs, Graph Theory Notes New York 55 (2008) 27-32.
19. Ş. B. Bozkurt, A. D. Güngör, B. Zhou, Note on the distance energy of graphs, MATCH Commun. Math. Comput. Chem. 64 (2010) 129-134.
20. D. Stevanović, G. Indulal, The distance spectrum and energy of the compositions of regular graphs, Appl. Math. Lett. 22 (2009) 1136-1140.
21. G. Indulal, A. Vijayakumar, A note on energy of some graphs, MATCH Commun. Math. Comput. Chem. 59 (2008) 269-274.
22. H. S. Ramane, D. S. Revankar, I. Gutman, H. B. Walikar, Distance spectra and distance energies of iterated line graphs of regular graphs, Publ. Inst. Math. (Beograd) 85 (2009) 39-46.
23. G. Indulal, I. Gutman, On the distance spectra of some graphs, Math. Commun. 13 (2008) 123-131.
24. D. Cvetković, M. Doob, I. Gutman, A. Torgašev, Recent Results in the Theory of Graph Spectra, North-Holland, Amsterdam, 1988.
25. R. Bapat, S. J. Kirkland, M. Neumann, On distance matrices and Laplacians, Linear Algebra Appl. 401 (2005) 193-209.
26. H. Hosoya, Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Japan 44 (1971) 2332-2339.
27. A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: theory and applications, Acta Appl. Math. 66 (2001) 211-249.
28. D. Cvetković, P. Rowlinson, S. Simić, Spectral Generalizations of Line Graphs. On Graphs with Least Eigenvalue -2, Cambridge Univ. Press, Cambridge, 2004.
29. I. Gutman, N. Trinajstić, Graph theory and molecular orbitais. III. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535-538.
30. I. Gutman, B. Ruščić, N. Trinajstić, C. F. Wilcox, Graph theory and molecular orbitais. XII. Acyclic polyenes, J. Phys. Chem. 62 (1975) 3399-3405.
31. S. Nikolić, G. Kovačević, A. Miličevič , N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003) 113-124.
32. I. Gutman, K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004) 83-92.
33. I. Gutman, The energy of a graph, Ber. Math.-Statist. Sekt. Forschungsz. Graz. 103 (1978) 1-22.
34. 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.
35. K. Fan, Maximum properties and inequalities for the eigenvalues of completely continuous operators, Proc. Nat. Acad. Sci. U.S.A. 37 (1951) 760-766.
36. J. Koolen, V. Moulton, Maximal energy graphs, Adv. Appl. Math. 26 (2001) 47-52.