28. Lovász L, Plummer MD (1986) Matching theory. North-Holland, Amsterdam
29. Zhang H (2006) Z-Transformation graphs of perfect matchings of plane bipartite graphs: a
survey. MATCH Commun Math Comput Chem 56:457–476
30. Vukičević D (2011) Applications of perfect matchings in chemistry. In: Dehmer M
(ed) Structural analysis of complex networks. Birkhäuser, Dordrecht, pp 463–482
31. Herndon WC (1973) Resonance energies of aromatic hydrocarbons. A quantitative test of
resonance theory. J Am Chem Soc 95:2404–2406
32. Simpson WT (1953) On the use of structures as an aid in understanding π -electron spectra.
J Am Chem Soc 75:597–603
33. Herndon WC (1974) Resonance theory and the enumeration of Kekulé structures. J Chem
Educ 51:10–15
34. Herndon WC, Ellzey ML (1974) Resonance theory. V. Resonance energies of benzenoid and
nonbenzenoid π systems. J Am Chem Soc 96:6631–6642
35. Herndon WC (1980) Structure–resonance theory—A review of applications to πhydrocarbon systems. Israel J Chem 20:270–275
36. Herndon WC (1981) Notes on valence bond theory, structure–resonance theory, and graph
theory. MATCH Commun Math Comput Chem 11:3–11
37. Klein DJ, Schmalz TG (1989) Exact ground state for a Herndon-Simpson model in
resonance–theoretic cluster expansion. Int J Quantum Chem 35:373–383
38. Gutman I, Cyvin SJ (1989) Introduction to the theory of benzenoid hydrocarbons. Springer,
Berlin
39. Hall GG (1991) Aromaticity measured by Kekulé structures. Int J Quantum Chem 39:605–
613
40. Randić M (2003) Aromaticity of polycyclic conjugated hydrocarbons. Chem Rev 103:3449–
3606
41. Gutman I, Stanković S (2007) Why is phenanthrene more stable than anthracene? Maced J
Chem Chem Engin 26:111–114
42. Swinborne-Sheldrake R, Herndon WC, Gutman I (1975) Kekulé structures and resonance
energies of benzenoid hydrocarbons. Tetrahedron Lett 16:755–758
43. Carter PC (1949) An empirical equation for the resonance energy of polycyclic aromatic
hydrocarbons. Trans Faraday Soc 45:597–602
44. Hall GG (1973) A graphical model of a class of molecules. Int J Math Educ Sci Technol
4:233–240
45. Gutman I, Trinajstić N, Wilcox CF (1975) Graph theory and molecular orbitals—X. The
number of Kekulé structures and the thermodynamic stability of conjugated systems.
Tetrahedron 31:143–146
46. Cioslowski J (1987) A unified theory of the stability of benzenoid hydrocarbons. Int J
Quantum Chem 31:581–590
47. Cioslowski J (1990) A final solution of the problem concerning the (N, M, K)-dependence of
the total π-electron energy of conjugated systems. MATCH Commun Math Comput Chem
25:83–93
48. Gutman I, Hall GG (1992) Linear dependence of total π-electron energy of benzenoid
hydrocarbons on Kekulé structure count. Int J Quantum Chem 41:667–672
49. Gutman I (1999) On the Hall rule in the theory of benzenoid hydrocarbons. Int J Quantum
Chem 74:627–632
50. Gutman I (1992) Total π-electron energy of benzenoid hydrocarbons. Topics Curr Chem
162:29–63
51. Gutman I (2005) Topology and stability of conjugated hydrocarbons. The dependence of
total π-electron energy on molecular topology. J Serb Chem Soc 70:441–456
52. Clar E, Stewart DG (1953) Aromatic hydrocarbons. XLV. Triangulene derivatives. J Am
Chem Soc 75:2667–2672
53. Clar E, Kemp W, Stewart DG (1958) The significance of Kekulé structures for the stability of
aromatic systems. Tetrahedron 3:325–333
316
I. Gutman and S. Radenković
29. Zhang H (2006) Z-Transformation graphs of perfect matchings of plane bipartite graphs: a
survey. MATCH Commun Math Comput Chem 56:457–476
30. Vukičević D (2011) Applications of perfect matchings in chemistry. In: Dehmer M
(ed) Structural analysis of complex networks. Birkhäuser, Dordrecht, pp 463–482
31. Herndon WC (1973) Resonance energies of aromatic hydrocarbons. A quantitative test of
resonance theory. J Am Chem Soc 95:2404–2406
32. Simpson WT (1953) On the use of structures as an aid in understanding π -electron spectra.
J Am Chem Soc 75:597–603
33. Herndon WC (1974) Resonance theory and the enumeration of Kekulé structures. J Chem
Educ 51:10–15
34. Herndon WC, Ellzey ML (1974) Resonance theory. V. Resonance energies of benzenoid and
nonbenzenoid π systems. J Am Chem Soc 96:6631–6642
35. Herndon WC (1980) Structure–resonance theory—A review of applications to πhydrocarbon systems. Israel J Chem 20:270–275
36. Herndon WC (1981) Notes on valence bond theory, structure–resonance theory, and graph
theory. MATCH Commun Math Comput Chem 11:3–11
37. Klein DJ, Schmalz TG (1989) Exact ground state for a Herndon-Simpson model in
resonance–theoretic cluster expansion. Int J Quantum Chem 35:373–383
38. Gutman I, Cyvin SJ (1989) Introduction to the theory of benzenoid hydrocarbons. Springer,
Berlin
39. Hall GG (1991) Aromaticity measured by Kekulé structures. Int J Quantum Chem 39:605–
613
40. Randić M (2003) Aromaticity of polycyclic conjugated hydrocarbons. Chem Rev 103:3449–
3606
41. Gutman I, Stanković S (2007) Why is phenanthrene more stable than anthracene? Maced J
Chem Chem Engin 26:111–114
42. Swinborne-Sheldrake R, Herndon WC, Gutman I (1975) Kekulé structures and resonance
energies of benzenoid hydrocarbons. Tetrahedron Lett 16:755–758
43. Carter PC (1949) An empirical equation for the resonance energy of polycyclic aromatic
hydrocarbons. Trans Faraday Soc 45:597–602
44. Hall GG (1973) A graphical model of a class of molecules. Int J Math Educ Sci Technol
4:233–240
45. Gutman I, Trinajstić N, Wilcox CF (1975) Graph theory and molecular orbitals—X. The
number of Kekulé structures and the thermodynamic stability of conjugated systems.
Tetrahedron 31:143–146
46. Cioslowski J (1987) A unified theory of the stability of benzenoid hydrocarbons. Int J
Quantum Chem 31:581–590
47. Cioslowski J (1990) A final solution of the problem concerning the (N, M, K)-dependence of
the total π-electron energy of conjugated systems. MATCH Commun Math Comput Chem
25:83–93
48. Gutman I, Hall GG (1992) Linear dependence of total π-electron energy of benzenoid
hydrocarbons on Kekulé structure count. Int J Quantum Chem 41:667–672
49. Gutman I (1999) On the Hall rule in the theory of benzenoid hydrocarbons. Int J Quantum
Chem 74:627–632
50. Gutman I (1992) Total π-electron energy of benzenoid hydrocarbons. Topics Curr Chem
162:29–63
51. Gutman I (2005) Topology and stability of conjugated hydrocarbons. The dependence of
total π-electron energy on molecular topology. J Serb Chem Soc 70:441–456
52. Clar E, Stewart DG (1953) Aromatic hydrocarbons. XLV. Triangulene derivatives. J Am
Chem Soc 75:2667–2672
53. Clar E, Kemp W, Stewart DG (1958) The significance of Kekulé structures for the stability of
aromatic systems. Tetrahedron 3:325–333
316
I. Gutman and S. Radenković