Mathematical Chemistry Works ‎of Dragos Cvetkovic

Document Type: Original Scientific Paper


Faculty of Science, University of Kragujevac, Kragujevac, Serbia


‎In addition to his countless contributions to spectral graph theory‎, some works of Dragos Cvetkovic are concerned with chemical problems‎. These are briefly outlined‎, ‎with emphasis on his collaboration with‎ the present author‎.


[1] K. Balinska, D. Cvetkovic, M. Lepovic and S. Simic, There are exactly 150
connected integral graphs up to 10 vertices, Univ. Beograd. Publ. Elektrotehn.
Fak. Ser. Mat. 10 (1999) 95–105.
[2] D. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs – Theory and Applications,
Third Edition, Johann Ambrosius Barth, Heidelberg, 1995.
[3] D. Cvetkovic, P. Rowlinson and S. Simic, An Introduction to the Theory of
Graph Spectra, London Mathematical Society Student Texts, 75, Cambridge
Univ. Press, Cambridge, 2010.
[4] D. M. Cvetkovic and I. Gutman, The algebraic multiplicity of the number
zero in the spectrum of a bipartite graph, Mat. Vesnik 9 (1972) 141–150.
[5] D. Cvetkovic, I. Gutman and N. Trinajstic, Graph theory and molecular
orbitals. II, Croat. Chem. Acta 44 (1972) 365–374.
[6] D. Cvetkovic, I. Gutman and N. Trinajstic, Graph theory and molecular
orbitals. IX. On the stability of cata-condensed hydrocarbons, Theor. Chim.
Acta 34 (1974) 129–136.
[7] D. Cvetkovic, I. Gutman and N. Trinajstic, Graphical studies on the relations
between the structure and reactivity of conjugated systems: The role of nonbonding
molecular orbitals, J. Mol. Struct. 28 (1975) 289–303.
[8] D. Cvetkovic and I. Gutman, Kekulé structures and topology. II. Catacondensed
systems, Croat. Chem. Acta 46 (1974) 15–23.
[9] D. Cvetkovic, I. Gutman and N. Trinajstic, Kekulé structures and topology,
Chem. Phys. Lett. 16 (1972) 614–616.
[10] D. Cvetkovic, I. Gutman and N. Trinajstic, Graph theory and molecular
orbitals. VII. The role of resonance structures, J. Chem. Phys. 61 (1974)
[11] D. Cvetkovic and P. Rowlinson, The largest eigenvalue of a graph: A survey,
Linear and Multilinear Algebra 28 (1990) 3–33.
[12] D. Cvetkovic, Graphs and their spectra, Publ. Elektrotehn. Fak. (Ser. Mat.
Fiz.) 354 (1971) 1–50.
[13] D. Cvetkovic and I. Gutman, Note on branching, Croat. Chem. Acta 49 (1977)

[14] D. Cvetkovic and S. Simic, Graph theoretic results obtained by the support
of the expert system “graph”, Bull. Cl. Sci. Math. Nat. Sci. Math. 19 (1994)
[15] D. Cvetkovic and I. Gutman, The computer system GRAPH: A useful tool
in chemical graph theory, J. Comput. Chem. 7 (1986) 640–644.
[16] D. Cvetkovic, P. W. Fowler, P. Rowlinson and D. Stevanovic, Constructing
fullerene graphs from their eigenvalues and angles, Linear Algebra Appl. 356
(2002) 37–56.
[17] D. Cvetkovic and D. Stevanovic, Spectral moments of fullerene graphs,
MATCH Commun. Math. Comput. Chem. 50 (2004) 63–72.
[18] D. Cvetkovic, Characterizing properties of some graph invariants related to
electron charges in the Hückel molecular orbital theory, in: P. Hansen, P.
Fowler, M. Zheng (Eds.), Discrete Mathematical Chemistry, American Mathematical
Society, Providence, RI, 2000, pp. 79–84.
[19] D. Cvetkovic and J. Grout, Graphs with extremal energy should have a small
number of distinct eigenvalues, Bull. Cl. Sci. Math. Nat. Sci. Math. 32 (2007)
[20] D. Cvetkovic, Z. Dražic, V. Kovacevic–Vujcic and M. Cangalovic, The traveling
salesman problem: the spectral radius and the length of an optimal tour,
Bull. Cl. Sci. Math. Nat. Sci. Math. 43 (2018) 17–26.

[21] D. Cvetkovic, Bichromaticity and graph spectrum, Matematicka Biblioteka,
(in Serbian) 41 (1969) 193–194.
[22] D. Cvetkovic, I. Gutman and N. Trinajstic, Conjugated molecules having
integral graph spectra, Chem. Phys. Lett. 29 (1974) 65–68.
[23] G. Caporossi, D. Cvetkovic, I. Gutman and P. Hansen, Variable neighborhood
search for extremal graphs. 2. Finding graphs with extremal energy, J. Chem.
Inf. Comput. Sci. 39 (1999) 984–996.
[24] C. A. Coulson, Notes on the secular determinant in molecular orbital theory,
Proc. Cambridge Phil. Soc. 46 (1950) 202–205.
[25] S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons,
Springer, Berlin, 1988.
[26] I. S. Dmitriev, Molecules without Chemical Bonds?, Himiya, Leningrad (in
Russian) 1980, Mir, Moscow (in English) 1981, Deutscher Verlag der Grundstoffindustrie,
Leipzig (in German) 1982.

[27] A. Graovac, I. Gutman, N. Trinajstic and T. Živkovic, Graph theory and
molecular orbitals. Application of Sachs theorem, Theor. Chim. Acta 26
(1972) 67–78.
[28] I. Gutman, Impact of the Sachs theorem on theoretical chemistry: A participant’s
testimony, MATCH Commun. Math. Comput. Chem. 48 (2003) 17–34.
[29] I. Gutman and D. Vidovic, Two early branching indices and the relation
between them, Theor. Chem. Acc. 108 (2002) 98–102.
[30] I. Gutman, The energy of a graph, Ber. Math.-Statist. Sekt. Forsch. Graz
103 (1978) 1–22.
[31] I. Gutman and B. Furtula, Survey of graph energies, Math. Interdisc. Res. 2
(2017) 85–129.
[32] Hs. H. Günthard and H. Primas, Zusammenhang von Graphentheorie und
MOâARTheorie von Molekeln mit Systemen konjugierter Bindungen, Helv.
Chim. Acta 39 (1956) 1645–1653.
[33] W. H. Haemers and Q. Xiang, Strongly regular graphs with parameters
(4m4; 2m4+m2;m4+m2;m4+m2) exist for all m > 1, European J. Combin.
31 (2010) 1553–1559.
[34] L. Lovász and J. Pelikán, On the eigenvalues of trees, Period. Math. Hungar.
3 (1973) 175–182.
[35] X. Li, Y. Shi and I. Gutman, Graph Energy, Springer, New York, 2012.
[36] R. B. Mallion and D. H. Rouvray, The golden jubilee of the Coulson–
Rushbrooke pairing theorem, J. Math. Chem. 5 (1990) 1–21.
[37] H. Sachs, Beziehungen zwischen den in einem Graphen enthaltenen Kreisen
und seinem charakteristischen Polynom, Publ. Math. Debrecen 11 (1964)

Volume 4, Issue 2
Special Issue: Spectral Graph Theory and Mathematical Chemistry with Connection to Computer Science
Autumn 2019
Pages 129-136