The energy change of weighted graphs

Linear Algebra and Its Applications

Volumn 435, Issue 10, 2011, Pages 2425-2431

  Gutman, Ivan ^a   Shao, Jia Yu ^b  

^a UNIVERSITY OF KRAGUJEVAC   (Serbia)

^b TONGJI UNIVERSITY   (China)

Author keywords

Energy (of graph); Graph spectrum; Singular value (of matrix); Weighted graph

Indexed keywords

ABSOLUTE VALUES; ADJACENCY MATRICES; EIGENVALUES; ENERGY (OF GRAPH); ENERGY CHANGES; GRAPH SPECTRA; SINGULAR VALUES; SUFFICIENT CONDITIONS; WEIGHTED GRAPH;

EIGENVALUES AND EIGENFUNCTIONS;

GRAPHIC METHODS;

EID: 79958777103     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2011.02.045     Document Type: Article

References (22)

1. J. Aihara General rules for constructing Hückel molecular orbital characteristic polynomials J. Am. Chem. Soc. 98 1976 6840 6844
2. S. Akbari, E. Ghorbani, and M. Oboudi Edge addition, singular values, and energy of graphs and matrices Linear Algebra Appl. 430 2009 2192 2199
3. C.A. Coulson, and H.C. Longuet-Higgins The electronic structure of conjugated systems. II. Unsaturated hydrocarbons and their hetero-derivatives Proc. Roy. Soc. London A192 1947 16 32
4. D.M. Cvetković, M. Doob, and H. Sachs Spectra of Graphs - Theory and Application 1980 Academic Press New York
5. J. Day, and W. So Singular value inequality and graph energy change Electron. J. Linear Algebra 16 2007 291 299
6. J. Day, and W. So Graph energy change due to edge deletion Linear Algebra Appl. 428 2008 2070 2078
7. K. Fan Maximum properties and inequalities for the eigenvalues of completely continuous operators Proc. Natl. Acad. Sci. USA 37 1951 760 766
8. I. Gutman Acyclic systems with extremal Hückel π-electron energy Theor. Chim. Acta 45 1977 79 87
9. I. Gutman The energy of a graph: old and new results A. Betten, A. Kohnert, R. Laue, A. Wassermann, Algebraic Combinatorics and Applications 2001 Springer-Verlag Berlin 196 211
10. A. Graovac, O.E. Polansky, N. Trinajstić, and N.N. Tyutyulkov Graph theory in chemistry. II. Graph-theoretical description of heteroconjugated molecules Z. Naturforsch. 30a 1975 1696 1699
11. 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 (Pubitemid 43166585)
12. I. Gutman, X. Li, and J. Zhang Graph energy M. Dehmer, F. Emmert-Streib, Analysis of Complex Networks. From Biology to Linguistics 2009 Wiley-VCH Weinheim 145 174
13. I. Gutman, and M. Mateljević Note on the Coulson integral formula J. Math. Chem. 39 2006 259 266 (Pubitemid 43375525)
14. I. Gutman, and O.E. Polansky Cyclic conjugation and the Hückel molecular orbital model Theor. Chim. Acta 60 1981 203 226
15. I. Gutman, and O.E. Polansky Mathematical Concepts in Organic Chemistry 1986 Springer-Verlag Berlin
16. R.B. Mallion, A.J. Schwenk, and N. Trinajstić A graphical study of heteroconjugated molecules Croat. Chem. Acta 46 1974 171 182
17. R.B. Mallion, N. Trinajstić, and A.J. Schwenk Graph theory in chemistry - generalization of Sachs' formula Z. Naturforsch. 29a 1974 1481 1484
18. M. Mateljević, and I. Gutman Note on the Coulson and Coulson-Jacobs integral formulas Match 59 2008 257 268
19. R.K. Mishra, and S.M. Patra Influence of the Hückel k parameter on the pairing of the eigenvaluesof heteroconjugated molecules J. Chem. Inf. Comput. Sci 37 1997 495 500 (Pubitemid 127603556)
20. V. Nikiforov The energy of graphs and matrices J. Math. Anal. Appl. 326 2007 1472 1475 (Pubitemid 44689172)
21. H.Y. Shan, and J.Y. Shao Graph energy change due to edge grafting operations and its application Match 64 2010 25 40
22. W. So, M. Robbiano, N.M.M. de Abreu, and I. Gutman Applications of a theorem by Ky Fan in the theory of graph energy Linear Algebra Appl. 432 2010 2163 2169