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2012 | OriginalPaper | Buchkapitel

2. The Chemical Connection

verfasst von : Xueliang Li, Yongtang Shi, Ivan Gutman

Erschienen in: Graph Energy

Verlag: Springer New York

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Abstract

Research on what we call the energy of a graph can be traced back to the 1940s or even to the 1930s. In the 1930s, the German scholar Erich Hückel put forward a method for finding approximate solutions of the Schrödinger equation of a class of organic molecules, the so-called conjugated hydrocarbons. Details of this approach, often referred to as the “Hückel molecular orbital (HMO) theory” can be found in appropriate textbooks [76, 101].

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Zurück zum Zitat I. Gutman, Generalizing the McClelland and Koolen–Moulton inequalities for total π-electron energy. Int. J. Chem. Model. 3, (2012) in press I. Gutman, Generalizing the McClelland and Koolen–Moulton inequalities for total π-electron energy. Int. J. Chem. Model. 3, (2012) in press
180.
Zurück zum Zitat I. Gutman, A.R. Ashrafi, G.H. Fath–Tabar, Equienergetic graphs. Farhang va Andishe-e-Riazi 15, 41–50 (1389) (in Persian, 1389 ∼ 2011) I. Gutman, A.R. Ashrafi, G.H. Fath–Tabar, Equienergetic graphs. Farhang va Andishe-e-Riazi 15, 41–50 (1389) (in Persian, 1389 ∼ 2011)
181.
Zurück zum Zitat I. Gutman, N. Cmiljanović, S. Milosavljević, S. Radenković, Effect of non-bonding molecular orbitals on total π-electron energy. Chem. Phys. Lett. 383, 171–175 (2004)CrossRef I. Gutman, N. Cmiljanović, S. Milosavljević, S. Radenković, Effect of non-bonding molecular orbitals on total π-electron energy. Chem. Phys. Lett. 383, 171–175 (2004)CrossRef
182.
Zurück zum Zitat I. Gutman, N. Cmiljanović, S. Milosavljević, S. Radenković, Dependence of total π-electron energy on the number of non-bonding molecular orbitals. Monatsh. Chem. 135, 765–772 (2004)CrossRef I. Gutman, N. Cmiljanović, S. Milosavljević, S. Radenković, Dependence of total π-electron energy on the number of non-bonding molecular orbitals. Monatsh. Chem. 135, 765–772 (2004)CrossRef
183.
Zurück zum Zitat I. Gutman, S.J. Cyvin, Introduction to the Theory of Benzenoid Hydrocarbons (Springer, Berlin, 1989)CrossRef I. Gutman, S.J. Cyvin, Introduction to the Theory of Benzenoid Hydrocarbons (Springer, Berlin, 1989)CrossRef
184.
Zurück zum Zitat I. Gutman, N.M.M. de Abreu, C.T.M. Vinagre, A.S. Bonifácio, S. Radenković, Relation between energy and Laplacian energy. MATCH Commun. Math. Comput. Chem. 59, 343–354 (2008)MathSciNetMATH I. Gutman, N.M.M. de Abreu, C.T.M. Vinagre, A.S. Bonifácio, S. Radenković, Relation between energy and Laplacian energy. MATCH Commun. Math. Comput. Chem. 59, 343–354 (2008)MathSciNetMATH
185.
Zurück zum Zitat I. Gutman, B. Furtula, H. Hua, Bipartite unicyclic graphs with maximal, second-maximal, and third-maximal energy. MATCH Commun. Math. Comput. Chem. 58, 85–92 (2007)MathSciNet I. Gutman, B. Furtula, H. Hua, Bipartite unicyclic graphs with maximal, second-maximal, and third-maximal energy. MATCH Commun. Math. Comput. Chem. 58, 85–92 (2007)MathSciNet
186.
Zurück zum Zitat I. Gutman, B. Furtula, D. Vidović, Coulson function and total π-electron energy. Kragujevac J. Sci. 24, 71–82 (2002) I. Gutman, B. Furtula, D. Vidović, Coulson function and total π-electron energy. Kragujevac J. Sci. 24, 71–82 (2002)
187.
Zurück zum Zitat I. Gutman, A. Graovac, S. Vuković, S. Marković, Some more isomer-undistinguishing approximate formulas for the total π-electron energy of benzenoid hydrocarbons. J. Serb. Chem. Soc. 54, 189–196 (1989) I. Gutman, A. Graovac, S. Vuković, S. Marković, Some more isomer-undistinguishing approximate formulas for the total π-electron energy of benzenoid hydrocarbons. J. Serb. Chem. Soc. 54, 189–196 (1989)
188.
Zurück zum Zitat I. Gutman, E. Gudiño, D. Quiroz, Upper bound for the energy of graphs with fixed second and fourth spectral moments. Kragujevac J. Math. 32, 27–35 (2009)MathSciNetMATH I. Gutman, E. Gudiño, D. Quiroz, Upper bound for the energy of graphs with fixed second and fourth spectral moments. Kragujevac J. Math. 32, 27–35 (2009)MathSciNetMATH
189.
Zurück zum Zitat I. Gutman, G.G. Hall, Linear dependence of total π-electron energy of benzenoid hydrocarbons on Kekulé structure count. Int. J. Quant. Chem. 41, 667–672 (1992)CrossRef I. Gutman, G.G. Hall, Linear dependence of total π-electron energy of benzenoid hydrocarbons on Kekulé structure count. Int. J. Quant. Chem. 41, 667–672 (1992)CrossRef
190.
Zurück zum Zitat I. Gutman, G.G. Hall, S. Marković, Z. Stanković, V. Radivojević, Effect of bay regions on the total π-electron energy of benzenoid hydrocarbons. Polyc. Arom. Comp. 2, 275–282 (1991)CrossRef I. Gutman, G.G. Hall, S. Marković, Z. Stanković, V. Radivojević, Effect of bay regions on the total π-electron energy of benzenoid hydrocarbons. Polyc. Arom. Comp. 2, 275–282 (1991)CrossRef
191.
Zurück zum Zitat I. Gutman, Y. Hou, Bipartite unicyclic graphs with greatest energy. MATCH Commun. Math. Comput. Chem. 43, 17–28 (2001)MathSciNetMATH I. Gutman, Y. Hou, Bipartite unicyclic graphs with greatest energy. MATCH Commun. Math. Comput. Chem. 43, 17–28 (2001)MathSciNetMATH
192.
Zurück zum Zitat I. Gutman, Y. Hou, H.B. Walikar, H.S. Ramane, P.R. Hampiholi, No Hückel graph is hyperenergetic. J. Serb. Chem. Soc. 65, 799–801 (2000) I. Gutman, Y. Hou, H.B. Walikar, H.S. Ramane, P.R. Hampiholi, No Hückel graph is hyperenergetic. J. Serb. Chem. Soc. 65, 799–801 (2000)
193.
Zurück zum Zitat I. Gutman, G. Indulal, R. Todeschini, Generalizing the McClelland bounds for total π-electron energy. Z. Naturforsch. 63a, 280–282 (2008) I. Gutman, G. Indulal, R. Todeschini, Generalizing the McClelland bounds for total π-electron energy. Z. Naturforsch. 63a, 280–282 (2008)
194.
Zurück zum Zitat I. Gutman, A. Kaplarević, A. Nikolić, An auxiliary function in the theory of total π-electron energy. Kragujevac J. Sci. 23, 75–88 (2001) I. Gutman, A. Kaplarević, A. Nikolić, An auxiliary function in the theory of total π-electron energy. Kragujevac J. Sci. 23, 75–88 (2001)
195.
Zurück zum Zitat I. Gutman, D. Kiani, M. Mirzakhah, On incidence energy of graphs. MATCH Commun. Math. Comput. Chem. 62, 573–580 (2009)MathSciNetMATH I. Gutman, D. Kiani, M. Mirzakhah, On incidence energy of graphs. MATCH Commun. Math. Comput. Chem. 62, 573–580 (2009)MathSciNetMATH
196.
197.
Zurück zum Zitat I. Gutman, A. Klobučar, S. Majstorović, C. Adiga, Biregular graphs whose energy exceeds the number of vertices. MATCH Commun. Math. Comput. Chem. 62, 499–508 (2009)MathSciNetMATH I. Gutman, A. Klobučar, S. Majstorović, C. Adiga, Biregular graphs whose energy exceeds the number of vertices. MATCH Commun. Math. Comput. Chem. 62, 499–508 (2009)MathSciNetMATH
198.
Zurück zum Zitat I. Gutman, J.H. Koolen, V. Moulton, M. Parac, T. Soldatović, D. Vidović, Estimating and approximating the total π-electron energy of benzenoid hydrocarbons. Z. Naturforsch. 55a, 507–512 (2000) I. Gutman, J.H. Koolen, V. Moulton, M. Parac, T. Soldatović, D. Vidović, Estimating and approximating the total π-electron energy of benzenoid hydrocarbons. Z. Naturforsch. 55a, 507–512 (2000)
199.
Zurück zum Zitat I. Gutman, X. Li, Y. Shi, J. Zhang, Hypoenergetic trees. MATCH Commun. Math. Comput. Chem. 60, 415–426 (2008)MathSciNetMATH I. Gutman, X. Li, Y. Shi, J. Zhang, Hypoenergetic trees. MATCH Commun. Math. Comput. Chem. 60, 415–426 (2008)MathSciNetMATH
200.
Zurück zum Zitat I. Gutman, X. Li, J. Zhang, in Graph Energy, ed. by M. Dehmer, F. Emmert–Streib. Analysis of Complex Networks. From Biology to Linguistics (Wiley–VCH, Weinheim, 2009), pp. 145–174 I. Gutman, X. Li, J. Zhang, in Graph Energy, ed. by M. Dehmer, F. Emmert–Streib. Analysis of Complex Networks. From Biology to Linguistics (Wiley–VCH, Weinheim, 2009), pp. 145–174
201.
Zurück zum Zitat I. Gutman, S. Marković, Topological properties of benzenoid systems. XLVIIIa. An empirical study of two contradictory formulas for total π-electron energy. MATCH Commun. Math. Comput. Chem. 25, 141–149 (1990) I. Gutman, S. Marković, Topological properties of benzenoid systems. XLVIIIa. An empirical study of two contradictory formulas for total π-electron energy. MATCH Commun. Math. Comput. Chem. 25, 141–149 (1990)
202.
Zurück zum Zitat I. Gutman, S. Marković, G.G. Hall, Revisiting a simple regularity for benzenoid hydrocarbons: Total π-electron energy versus the number of Kekulé structures. Chem. Phys. Lett. 234, 21–24 (1995)CrossRef I. Gutman, S. Marković, G.G. Hall, Revisiting a simple regularity for benzenoid hydrocarbons: Total π-electron energy versus the number of Kekulé structures. Chem. Phys. Lett. 234, 21–24 (1995)CrossRef
203.
Zurück zum Zitat I. Gutman, S. Marković, M. Marinković, Investigation of the Cioslowski formula. MATCH Commun. Math. Comput. Chem. 22, 277–284 (1987) I. Gutman, S. Marković, M. Marinković, Investigation of the Cioslowski formula. MATCH Commun. Math. Comput. Chem. 22, 277–284 (1987)
204.
Zurück zum Zitat I. Gutman, S. Marković, A.V. Teodorović, Ž. Bugarčić, Isomer–undistinguishing approximate formulas for the total π-electron energy of benzenoid hydrocarbons. J. Serb. Chem. Soc. 51, 145–149 (1986) I. Gutman, S. Marković, A.V. Teodorović, Ž. Bugarčić, Isomer–undistinguishing approximate formulas for the total π-electron energy of benzenoid hydrocarbons. J. Serb. Chem. Soc. 51, 145–149 (1986)
205.
Zurück zum Zitat I. Gutman, S. Marković, A. Vesović, E. Estrada, Approximating total π-electron energy in terms of spectral moments. A quantitative approach. J. Serb. Chem. Soc. 63, 639–646 (1998) I. Gutman, S. Marković, A. Vesović, E. Estrada, Approximating total π-electron energy in terms of spectral moments. A quantitative approach. J. Serb. Chem. Soc. 63, 639–646 (1998)
206.
Zurück zum Zitat I. Gutman, S. Marković, D. Vukićević, A. Stajković, The dependence of total π-electron energy of large benzenoid hydrocarbons on the number of Kekulé structures is non-linear. J. Serb. Chem. Soc. 60, 93–98 (1995) I. Gutman, S. Marković, D. Vukićević, A. Stajković, The dependence of total π-electron energy of large benzenoid hydrocarbons on the number of Kekulé structures is non-linear. J. Serb. Chem. Soc. 60, 93–98 (1995)
208.
Zurück zum Zitat I. Gutman, M. Milun, N. Trinajstić, Comment on the paper: “Properties of the latent roots of a matrix. Estimation of π-electron energies” ed. by B.J. McClelland. J. Chem. Phys. 59, 2772–2774 (1973) I. Gutman, M. Milun, N. Trinajstić, Comment on the paper: “Properties of the latent roots of a matrix. Estimation of π-electron energies” ed. by B.J. McClelland. J. Chem. Phys. 59, 2772–2774 (1973)
209.
Zurück zum Zitat I. Gutman, M. Milun, N. Trinajstić, Graph theory and molecular orbitals. 19. Nonparametric resonance energies of arbitrary conjugated systems. J. Am. Chem. Soc. 99, 1692–1704 (1977) I. Gutman, M. Milun, N. Trinajstić, Graph theory and molecular orbitals. 19. Nonparametric resonance energies of arbitrary conjugated systems. J. Am. Chem. Soc. 99, 1692–1704 (1977)
210.
Zurück zum Zitat I. Gutman, L. Nedeljković, A.V. Teodorović, Topological formulas for total π-electron energy of benzenoid hydrocarbons – a comparative study. Bull. Soc. Chim. Beograd 48, 495–500 (1983) I. Gutman, L. Nedeljković, A.V. Teodorović, Topological formulas for total π-electron energy of benzenoid hydrocarbons – a comparative study. Bull. Soc. Chim. Beograd 48, 495–500 (1983)
211.
Zurück zum Zitat I. Gutman, A. Nikolić, Ž. Tomović, A concealed property of total π-electron energy. Chem. Phys. Lett. 349, 95–98 (2001)CrossRef I. Gutman, A. Nikolić, Ž. Tomović, A concealed property of total π-electron energy. Chem. Phys. Lett. 349, 95–98 (2001)CrossRef
212.
Zurück zum Zitat I. Gutman, L. Pavlović, The energy of some graphs with large number of edges. Bull. Acad. Serbe Sci. Arts. (Cl. Math. Natur.) 118, 35–50 (1999) I. Gutman, L. Pavlović, The energy of some graphs with large number of edges. Bull. Acad. Serbe Sci. Arts. (Cl. Math. Natur.) 118, 35–50 (1999)
213.
Zurück zum Zitat I. Gutman, S. Petrović, On total π-electron energy of benzenoid hydrocarbons. Chem. Phys. Lett. 97, 292–294 (1983)CrossRef I. Gutman, S. Petrović, On total π-electron energy of benzenoid hydrocarbons. Chem. Phys. Lett. 97, 292–294 (1983)CrossRef
214.
Zurück zum Zitat I. Gutman, P. Petković, P.V. Khadikar, Bounds for the total π-electron energy of phenylenes. Rev. Roum. Chim. 41, 637–643 (1996) I. Gutman, P. Petković, P.V. Khadikar, Bounds for the total π-electron energy of phenylenes. Rev. Roum. Chim. 41, 637–643 (1996)
215.
Zurück zum Zitat I. Gutman, O.E. Polansky, Cyclic conjugation and the Hückel molecular orbital model. Theor. Chim. Acta 60, 203–226 (1981) I. Gutman, O.E. Polansky, Cyclic conjugation and the Hückel molecular orbital model. Theor. Chim. Acta 60, 203–226 (1981)
216.
Zurück zum Zitat I. Gutman, O.E. Polansky, Mathematical Concepts in Organic Chemistry (Springer, Berlin, 1986)MATHCrossRef I. Gutman, O.E. Polansky, Mathematical Concepts in Organic Chemistry (Springer, Berlin, 1986)MATHCrossRef
217.
Zurück zum Zitat I. Gutman, S. Radenković, Extending and modifying the Hall rule. Chem. Phys. Lett. 423, 382–385 (2006)CrossRef I. Gutman, S. Radenković, Extending and modifying the Hall rule. Chem. Phys. Lett. 423, 382–385 (2006)CrossRef
218.
Zurück zum Zitat I. Gutman, S. Radenković, Hypoenergetic molecular graphs. Indian J. Chem. 46A, 1733–1736 (2007) I. Gutman, S. Radenković, Hypoenergetic molecular graphs. Indian J. Chem. 46A, 1733–1736 (2007)
219.
Zurück zum Zitat I. Gutman, S. Radenković, N. Li, S. Li, Extremal energy of trees. MATCH Commun. Math. Comput. Chem. 59, 315–320 (2008)MathSciNetMATH I. Gutman, S. Radenković, N. Li, S. Li, Extremal energy of trees. MATCH Commun. Math. Comput. Chem. 59, 315–320 (2008)MathSciNetMATH
220.
Zurück zum Zitat I. Gutman, M. Rašković, Monte Carlo approach to total π-electron energy of conjugated hydrocarbons. Z. Naturforsch. 40a, 1059–1061 (1985) I. Gutman, M. Rašković, Monte Carlo approach to total π-electron energy of conjugated hydrocarbons. Z. Naturforsch. 40a, 1059–1061 (1985)
221.
Zurück zum Zitat I. Gutman, M. Robbiano, E. Andrade–Martins, D.M. Cardoso, L. Medina, O. Rojo, Energy of line graphs. Lin. Algebra Appl. 433, 1312–1323 (2010) I. Gutman, M. Robbiano, E. Andrade–Martins, D.M. Cardoso, L. Medina, O. Rojo, Energy of line graphs. Lin. Algebra Appl. 433, 1312–1323 (2010)
222.
Zurück zum Zitat I. Gutman, B. Ruščić, N. Trinajstić, C.F. Wilcox, Graph theory and molecular orbitals. XII. Acyclic polyenes. J. Chem. Phys. 62, 3399–3405 (1975) I. Gutman, B. Ruščić, N. Trinajstić, C.F. Wilcox, Graph theory and molecular orbitals. XII. Acyclic polyenes. J. Chem. Phys. 62, 3399–3405 (1975)
224.
Zurück zum Zitat I. Gutman, T. Soldatović, Novel approximate formulas for the total π-electron energy of benzenoid hydrocarbons. Bull. Chem. Technol. Maced. 19, 17–20 (2000) I. Gutman, T. Soldatović, Novel approximate formulas for the total π-electron energy of benzenoid hydrocarbons. Bull. Chem. Technol. Maced. 19, 17–20 (2000)
225.
Zurück zum Zitat I. Gutman, T. Soldatović, (n, m)-Type approximations for total π-electron energy of benzenoid hydrocarbons. MATCH Commun. Math. Comput. Chem. 44, 169–182 (2001) I. Gutman, T. Soldatović, (n, m)-Type approximations for total π-electron energy of benzenoid hydrocarbons. MATCH Commun. Math. Comput. Chem. 44, 169–182 (2001)
226.
Zurück zum Zitat I. Gutman, T. Soldatović, On a class of approximate formulas for total π-electron energy of benzenoid hydrocarbons. J. Serb. Chem. Soc. 66, 101–106 (2001) I. Gutman, T. Soldatović, On a class of approximate formulas for total π-electron energy of benzenoid hydrocarbons. J. Serb. Chem. Soc. 66, 101–106 (2001)
227.
Zurück zum Zitat I. Gutman, T. Soldatović, A. Graovac, S. Vuković, Approximating the total π-electron energy by means of spectral moments. Chem. Phys. Lett. 334, 168–172 (2001)CrossRef I. Gutman, T. Soldatović, A. Graovac, S. Vuković, Approximating the total π-electron energy by means of spectral moments. Chem. Phys. Lett. 334, 168–172 (2001)CrossRef
228.
Zurück zum Zitat I. Gutman, T. Soldatović, M. Petković, A new upper bound and approximation for total π-electron energy. Kragujevac J. Sci. 23, 89–98 (2001) I. Gutman, T. Soldatović, M. Petković, A new upper bound and approximation for total π-electron energy. Kragujevac J. Sci. 23, 89–98 (2001)
229.
Zurück zum Zitat I. Gutman, T. Soldatović, D. Vidović, The energy of a graph and its size dependence. A Monte Carlo approach. Chem. Phys. Lett. 297, 428–432 (1998) I. Gutman, T. Soldatović, D. Vidović, The energy of a graph and its size dependence. A Monte Carlo approach. Chem. Phys. Lett. 297, 428–432 (1998)
230.
Zurück zum Zitat I. Gutman, A. Stajković, S. Marković, P. Petković, Dependence of total π-electron energy of phenylenes on Kekulé structure count. J. Serb. Chem. Soc. 59, 367–373 (1994) I. Gutman, A. Stajković, S. Marković, P. Petković, Dependence of total π-electron energy of phenylenes on Kekulé structure count. J. Serb. Chem. Soc. 59, 367–373 (1994)
231.
Zurück zum Zitat I. Gutman, S. Stanković, J. Durdević, B. Furtula, On the cycle–dependence of topological resonance energy. J. Chem. Inf. Model. 47, 776–781 (2007)CrossRef I. Gutman, S. Stanković, J. Durdević, B. Furtula, On the cycle–dependence of topological resonance energy. J. Chem. Inf. Model. 47, 776–781 (2007)CrossRef
232.
Zurück zum Zitat I. Gutman, D. Stevanović, S. Radenković, S. Milosavljević, N. Cmiljanović, Dependence of total π-electron energy on large number of non-bonding molecular orbitals. J. Serb. Chem. Soc. 69, 777–782 (2004)CrossRef I. Gutman, D. Stevanović, S. Radenković, S. Milosavljević, N. Cmiljanović, Dependence of total π-electron energy on large number of non-bonding molecular orbitals. J. Serb. Chem. Soc. 69, 777–782 (2004)CrossRef
233.
Zurück zum Zitat I. Gutman, A.V. Teodorović, Ž. Bugarčić, On some topological formulas for total π-electron energy of benzenoid molecules. Bull. Soc. Chim. Beograd 49, 521–525 (1984) I. Gutman, A.V. Teodorović, Ž. Bugarčić, On some topological formulas for total π-electron energy of benzenoid molecules. Bull. Soc. Chim. Beograd 49, 521–525 (1984)
234.
Zurück zum Zitat I. Gutman, A.V. Teodorović, L. Nedeljković, Topological properties of benzenoid systems. Bounds and approximate formulae for total π-electron energy. Theor. Chim. Acta 65, 23–31 (1984) I. Gutman, A.V. Teodorović, L. Nedeljković, Topological properties of benzenoid systems. Bounds and approximate formulae for total π-electron energy. Theor. Chim. Acta 65, 23–31 (1984)
235.
Zurück zum Zitat I. Gutman, Ž. Tomović, Total π-electron energy of phenylenes: Bounds and approximate expressions. Monatsh. Chem. 132, 1023–1029 (2001)CrossRef I. Gutman, Ž. Tomović, Total π-electron energy of phenylenes: Bounds and approximate expressions. Monatsh. Chem. 132, 1023–1029 (2001)CrossRef
236.
Zurück zum Zitat I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17, 535–538 (1972) I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17, 535–538 (1972)
237.
Zurück zum Zitat I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. The loop rule. Chem. Phys. Lett. 20, 257–260 (1973) I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. The loop rule. Chem. Phys. Lett. 20, 257–260 (1973)
238.
Zurück zum Zitat I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. Topics Curr. Chem. 42, 49–93 (1973) I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. Topics Curr. Chem. 42, 49–93 (1973)
239.
Zurück zum Zitat I. Gutman, L. Türker, Approximating the total π-electron energy of benzenoid hydrocarbons: Some new estimates of (n, m)-type. Indian J. Chem. 32A, 833–836 (1993) I. Gutman, L. Türker, Approximating the total π-electron energy of benzenoid hydrocarbons: Some new estimates of (n, m)-type. Indian J. Chem. 32A, 833–836 (1993)
240.
Zurück zum Zitat I. Gutman, L. Türker, J.R. Dias, Another upper bound for total π-electron energy of alternant hydrocarbons. MATCH Commun. Math. Comput. Chem. 19, 147–161 (1986) I. Gutman, L. Türker, J.R. Dias, Another upper bound for total π-electron energy of alternant hydrocarbons. MATCH Commun. Math. Comput. Chem. 19, 147–161 (1986)
241.
Zurück zum Zitat I. Gutman, D. Utvić, A.K. Mukherjee, A class of topological formulas for total π-electron energy. J. Serb. Chem. Soc. 56, 59–63 (1991) I. Gutman, D. Utvić, A.K. Mukherjee, A class of topological formulas for total π-electron energy. J. Serb. Chem. Soc. 56, 59–63 (1991)
242.
Zurück zum Zitat I. Gutman, D. Vidović, Quest for molecular graphs with maximal energy: A computer experiment. J. Chem. Inf. Comput. Sci. 41, 1002–1005 (2001)CrossRef I. Gutman, D. Vidović, Quest for molecular graphs with maximal energy: A computer experiment. J. Chem. Inf. Comput. Sci. 41, 1002–1005 (2001)CrossRef
243.
Zurück zum Zitat I. Gutman, D. Vidović, Conjugated molecules with maximal total π-electron energy. Bull. Acad. Serbe Sci. Arts (Cl. Math. Natur.) 124, 1–7 (2003) I. Gutman, D. Vidović, Conjugated molecules with maximal total π-electron energy. Bull. Acad. Serbe Sci. Arts (Cl. Math. Natur.) 124, 1–7 (2003)
244.
Zurück zum Zitat I. Gutman, D. Vidović, N. Cmiljanović, S. Milosavljević, S. Radenković, Graph energy – A useful molecular structure-descriptor. Indian J. Chem. 42A, 1309–1311 (2003) I. Gutman, D. Vidović, N. Cmiljanović, S. Milosavljević, S. Radenković, Graph energy – A useful molecular structure-descriptor. Indian J. Chem. 42A, 1309–1311 (2003)
245.
Zurück zum Zitat I. Gutman, D. Vidović, H. Hosoya, The relation between the eigenvalue sum and the topological index Z revisited. Bull. Chem. Soc. Jpn. 75, 1723–1727 (2002)CrossRef I. Gutman, D. Vidović, H. Hosoya, The relation between the eigenvalue sum and the topological index Z revisited. Bull. Chem. Soc. Jpn. 75, 1723–1727 (2002)CrossRef
246.
Zurück zum Zitat I. Gutman, D. Vidović, T. Soldatović, Modeling the dependence of the π-electron energy on the size of conjugated molecules. A Monte Carlo approach. ACH – Models Chem. 136, 599–608 (1999) I. Gutman, D. Vidović, T. Soldatović, Modeling the dependence of the π-electron energy on the size of conjugated molecules. A Monte Carlo approach. ACH – Models Chem. 136, 599–608 (1999)
247.
Zurück zum Zitat I. Gutman, S. Zare Firoozabadi, J.A. de la Penña, J. Rada, On the energy of regular graphs. MATCH Commun. Math. Comput. Chem. 57, 435–442 (2007)MathSciNetMATH I. Gutman, S. Zare Firoozabadi, J.A. de la Penña, J. Rada, On the energy of regular graphs. MATCH Commun. Math. Comput. Chem. 57, 435–442 (2007)MathSciNetMATH
248.
Zurück zum Zitat I. Gutman, F. Zhang, On the quasiordering of bipartite graphs. Publ. Inst. Math. (Belgrade) 40, 11–15 (1986)MathSciNet I. Gutman, F. Zhang, On the quasiordering of bipartite graphs. Publ. Inst. Math. (Belgrade) 40, 11–15 (1986)MathSciNet
249.
251.
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Metadaten
Titel
The Chemical Connection
verfasst von
Xueliang Li
Yongtang Shi
Ivan Gutman
Copyright-Jahr
2012
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-4220-2_2