Some graphs are more strongly-isospectral than others

Match

Volumn 63, Issue 3, 2010, Pages 737-750

  Randić, Milan ^a,c   Horvat, Boris ^b   Pisanski, Tomaz ^b  

^a NATIONAL INSTITUTE OF CHEMISTRY   (Slovenia)

^b UNIVERSITY OF LJUBLJANA   (Slovenia)

^c DRAKE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77953263397     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (41)

1. V. L. Collatz and U. Sinogowitz, Spectrum enlicher graphen, Abh. Math. Sent. Univ. Hamburg 21 (1957) 63-77.
2. D. Cvetković, M. Doob and H. Sachs, Spectra of Graphs, Johann Ambrosius Barth: Heidelberg, 1995.
3. nd ed., CRC Press, Boca Raton, FL. 1992.
4. E. Hückel, Quantentheoretische Beitrage zum Benzolproblem. I. Die Elektronenkonfiguration des Benzols und verwandeter Verbindungen, Zeit. F. Phys. 70 (1931) 204-286.
5. M. Randić, Conjugated circuits and resonance energies of benzenoid hydrocarbons, Chem. Phys. Lett. 38 (1976) 68-70.
6. M. Randić, Aromaticity and conjugation, J. Am. Chem. Soc. 99 (1997) 444-450.
7. M. Randić, Aromaticity of polycyclic conjugated hydrocarbons, Chem. Rev. 103 (2003) 3449-3605.
8. T. P. Živković, reported at the Quantum Chemistry School, Repino, near St. Petersburg, Russia (then Leningrad, U. S. S. R.), December 1973.
9. C. A. Coulson and A. Streitwieser, Dictionary of π-Electron Calculations, Freeman, San Francisco, 1965.
10. D. J. Klein, T. G. Schmalz, W. A. Seitz, and G. E. Hite, Overview of Hückel- and resonance-theoretic approaches to π-network polymers. Int. J. Quantum Chem: Quantum Chem. Symp. 19 (1986) 707-718.
11. H. Hosoya, From how to why. Graph-Theoretical verification of quantum mechanical aspects of π-electron behaviors in conjugated systems, Bull. Chem. Soc. Japan 76 (2003) 2233-2252.
12. D. J. Klein and N. Trinajstić, Foundations of conjugated-circuits models, Pure & Appl. Chem. 61 (1989) 2107-2115.
13. N. Trinajstić, D. Plavšić and D. J. Klein, The conjugated-circuit model revisited, Croat. Chem. Acta 62 (1989) 711-718.
14. G. E. Hite, T. P. Živković, and D. J. Klein, Conjugated circuit theory for graphite, Theor. Chim. Acta 74 (1988) 349-361.
15. D. J. Klein, W. A. Seitz, and T. G. Schmalz, Conjugated circuits computations for conjugated hydrocarbons, in: Computational Chemical Graph Theory, D. H. Rouvray, Ed., Nova Science Pub., New York, 1990.
16. D. J. Klein and X. Liu, Many-body conjugated circuit computations, J. Comput. Chem. 12 (1991) 1260-1264.
17. D. J. Klein, Aromaticity via Kekulé structures and conjugated circuits, J. Chem. Educ. 69 (1992) 691-694.
18. H. Zhu, A. T. Balaban, D. J. Klein and T. P. Živković, Conjugated-circuit computations on two-dimensional carbon networks, J. Chem. Phys. 101 (1994) 5281-5292.
19. H. Zhu and D. J. Klein, Conjugated circuits for polymers, MATCH Commun. Math Chem. 31 (1994) 205-224.
20. D. J. Klein, Inter-relations between VB & MO theories for organic π-networks, Theoretical Organic Chemistry (C. Párkányi, Ed.), Theoretical and Computational Chemistry 5 (1998) 33-50.
21. M. Randić, N. Trinajstić and T. Živković, Molecular graphs having identical spectra, J. Chem. Soc. - Faraday Transactions II 72 (1976) 244-256.
22. M. Randić and A. F. Kleiner, On the construction of endospectral graphs, Ann. New York Acad. Sci. 555 (1989) 320-331.
23. J. V. Knop, W. R. Müller, K. Szymanski, N. Trinajstić, A. F. Kleiner and M. Randić, On irreducible endospectral graphs, J. Math. Phys. 27 (1986) 2601-2612.
24. R. C. Read and D. G. Corneil. The graph isomorphism disease, J. Graph Theory 1 (1977) 339-363.
25. G. Gati, Further annotated bibliography on the isomorphism disease, J. Graph Theory 3 (1979) 95-110.
26. H. Hosoya, U. Nagashima and S. Hyugaji, Topological twin graphs. Smallest pair of isospectral polyhedral graphs with eight vertices, J. Chem. Inf. Comput. Sci. 34 (1994) 428-431.
27. H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17-20.
28. H. Hosoya, Topological index. A newly proposed quantity characterizing topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Jpn. 44 (1971) 2332-2339.
29. M. Randić, Characterization of molecular branching, J. Am. Chem. Soc. 97 (1975) 6609-6615.
30. A. R. Katritzky, V. Lobanov, and M. Karelson, CODESSA {Comprehensive Descriptors for Structural and Statistical Analysis); University of Florida, Gainesville, FL, 1994.
31. G. Jaklić, T. Pisanski and M. Randić. On description of biological sequences by spectral properties of line distance matrices, MATCH Commun. Math. Comput. Chem. 58 (2007) 301-307.
32. D. Janežić, A. Miličević, S. Nikolić and N. Trinajstić, Graph-Theoretical Matrices in Chemistry, Univ. Kragujevac, Kragujevac, 2007.
33. C. R. Johnson and M. Newman, A note on cospectral graphs. J. Comb. Theory B 28 (1980) 96-103.
34. M. Randić, T. Pisanski, M. Nović and D. Plavšić, Novel graph distance matrix, J. Comput. Chem. (in press).
35. B. D. McKay, On the spectral characterization of trees, Ars Combinatorica 3 (1977) 219-232.
36. M. Randić and D. Plavšić, (work in progress).
37. B. Horvat, T. Pisanski and M. Randić, Terminal polynomials and star-like graphs, MATCH Commun. Math. Comput. Chem. 60 (2008) 493-512.
38. B. Horvat, On the calculation of the terminal polynomial of a star-like graph, Croat. Chem. Acta 82 (2009) (to appear).
39. M. E. Fisher, On hearing the shape of a drum, J. Comb. Theory B 1 (1966) 105-125.
40. M. Randić, M. Nović and M. Vračko, On novel representation of proteins based on amino acids adjacency matrix, SAR & QSAR in Environ. Res. 19 (2008) 339-349.
41. T. Pisanski and J. Shawe-Taylor, Characterizing graph drawing with eigenvectors, J. Chem. Inf. Comp. Sci. 40 (2000) 567-571.