Skip to main content

Tipp

Weitere Artikel dieser Ausgabe durch Wischen aufrufen

Erschienen in: Journal of Applied Mathematics and Computing 1-2/2019

07.03.2018 | Original Research

Wiener index of certain families of hexagonal chains

verfasst von: Andrey A. Dobrynin, Ehsan Estaji

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2019

Einloggen

Abstract

The Wiener index is a topological index of a molecule, defined as the sum of distances between all pairs of vertices in the chemical graph representing the non-hydrogen atoms in the molecule. Hexagonal chains consist of hexagonal rings connected with each other by edges. This class of graphs contains molecular graphs of unbranched catacondensed benzenoid hydrocarbons. A segment of a chain is its maximal subchain with linear connected hexagons. Chains with segments of equal lengths can be coded by binary words. Formulas for the sums of Wiener indices of hexagonal chains of some families are derived and computational examples are presented.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Balaban, A.T.: Chemical graphs. L. Symmetry and enumeration of fibonacenes (unbranched catacondensed benzenoids isoarithmic with helicenes and zigzag catafusenes. MATCH Commun. Math. Comput. Chem. 24, 9–38 (1989) MATH Balaban, A.T.: Chemical graphs. L. Symmetry and enumeration of fibonacenes (unbranched catacondensed benzenoids isoarithmic with helicenes and zigzag catafusenes. MATCH Commun. Math. Comput. Chem. 24, 9–38 (1989) MATH
2.
Zurück zum Zitat Balaban, A.T., Motoc, I., Bonchev, D., Mekenyan, O.: Topological indices for structure–activity correlations. Top. Curr. Chem. 114, 21–55 (1983) CrossRef Balaban, A.T., Motoc, I., Bonchev, D., Mekenyan, O.: Topological indices for structure–activity correlations. Top. Curr. Chem. 114, 21–55 (1983) CrossRef
3.
Zurück zum Zitat Canfield, E.R., Robinson, R.W., Rouvray, D.H.: Determination of the Wiener molecular branching index for the general tree. J. Comput. Chem. 6, 598–609 (1985) MathSciNetCrossRef Canfield, E.R., Robinson, R.W., Rouvray, D.H.: Determination of the Wiener molecular branching index for the general tree. J. Comput. Chem. 6, 598–609 (1985) MathSciNetCrossRef
4.
Zurück zum Zitat Dehmer, M., Emmert-Streib, F. (eds.): Quantitative Graph Theory: Mathematical Foundations and Applications, Discrete Mathematics and Its Applications. Chapman and Hall/CRC, London (2014) Dehmer, M., Emmert-Streib, F. (eds.): Quantitative Graph Theory: Mathematical Foundations and Applications, Discrete Mathematics and Its Applications. Chapman and Hall/CRC, London (2014)
5.
Zurück zum Zitat Devillers, J., Balaban, A.T. (eds.): Topological Indices and Related Descriptors in QSAR and QSPR. Gordon and Breach, Reading (1999) Devillers, J., Balaban, A.T. (eds.): Topological Indices and Related Descriptors in QSAR and QSPR. Gordon and Breach, Reading (1999)
6.
Zurück zum Zitat Diudea, M.V. (ed.): QSPR/QSAR Studies by Molecular Descriptors. Nova, Huntington (2001) Diudea, M.V. (ed.): QSPR/QSAR Studies by Molecular Descriptors. Nova, Huntington (2001)
7.
Zurück zum Zitat Dobrynin, A.A., Entringer, R., Gutman, I.: Wiener index for trees: theory and applications. Acta Appl. Math. 66(3), 211–249 (2001) MathSciNetCrossRefMATH Dobrynin, A.A., Entringer, R., Gutman, I.: Wiener index for trees: theory and applications. Acta Appl. Math. 66(3), 211–249 (2001) MathSciNetCrossRefMATH
8.
Zurück zum Zitat Dobrynin, A.A., Gutman, I., Klavžar, S., Žigert, P.: Wiener index of hexagonal systems. Acta Appl. Math. 72(3), 247–294 (2002) MathSciNetCrossRefMATH Dobrynin, A.A., Gutman, I., Klavžar, S., Žigert, P.: Wiener index of hexagonal systems. Acta Appl. Math. 72(3), 247–294 (2002) MathSciNetCrossRefMATH
9.
Zurück zum Zitat Dobrynin, A.A.: On the Wiener index of fibonacenes. MATCH Commun. Math. Comput. Chem. 64(3), 707–726 (2010) MathSciNetMATH Dobrynin, A.A.: On the Wiener index of fibonacenes. MATCH Commun. Math. Comput. Chem. 64(3), 707–726 (2010) MathSciNetMATH
10.
Zurück zum Zitat Dobrynin, A.A.: On the Wiener index of certain families of fibonacenes. MATCH Commun. Math. Comput. Chem. 70(2), 565–574 (2013) MathSciNetMATH Dobrynin, A.A.: On the Wiener index of certain families of fibonacenes. MATCH Commun. Math. Comput. Chem. 70(2), 565–574 (2013) MathSciNetMATH
11.
Zurück zum Zitat Dobrynin, A.A.: Wiener index of hexagonal chains with segments of equal length. In: Dehmer, M., Emmert-Streib, F. (eds.) Quantitative Graph Theory: Mathematical Foundations and Applications, Discrete Mathematics and Its Applications, pp. 81–109. Chapman and Hall/CRC, London (2014) CrossRef Dobrynin, A.A.: Wiener index of hexagonal chains with segments of equal length. In: Dehmer, M., Emmert-Streib, F. (eds.) Quantitative Graph Theory: Mathematical Foundations and Applications, Discrete Mathematics and Its Applications, pp. 81–109. Chapman and Hall/CRC, London (2014) CrossRef
12.
Zurück zum Zitat Entringer, R.C.: Distance in graphs: trees. J. Combin. Math. Combin. Comput. 24, 65–84 (1997) MathSciNetMATH Entringer, R.C.: Distance in graphs: trees. J. Combin. Math. Combin. Comput. 24, 65–84 (1997) MathSciNetMATH
13.
Zurück zum Zitat Gutman, I.: Topological properties of benzenoid systems. Topics Curr. Chem. 162, 21–28 (1992) Gutman, I.: Topological properties of benzenoid systems. Topics Curr. Chem. 162, 21–28 (1992)
14.
Zurück zum Zitat Gutman, I., Cyvin, S.J.: Introduction to the Theory of Benzenoid Hydrocarbons. Springer, Berlin (1989) CrossRefMATH Gutman, I., Cyvin, S.J.: Introduction to the Theory of Benzenoid Hydrocarbons. Springer, Berlin (1989) CrossRefMATH
15.
Zurück zum Zitat Gutman, I., Klavžar, S.: Chemical graph theory of fibonacenes. MATCH Commun. Math. Comput. Chem. 55, 39–54 (2006) MathSciNetMATH Gutman, I., Klavžar, S.: Chemical graph theory of fibonacenes. MATCH Commun. Math. Comput. Chem. 55, 39–54 (2006) MathSciNetMATH
16.
Zurück zum Zitat Gutman, I., Polansky, O.E.: Mathematical Concepts in Organic Chemistry. Springer, Berlin (1986) CrossRefMATH Gutman, I., Polansky, O.E.: Mathematical Concepts in Organic Chemistry. Springer, Berlin (1986) CrossRefMATH
17.
Zurück zum Zitat Gutman, I., Yeh, Y.N., Lee, S.L., Luo, Y.L.: Some recent results in the theory of the Wiener number. Indian J. Chem. 32A, 651–661 (1993) Gutman, I., Yeh, Y.N., Lee, S.L., Luo, Y.L.: Some recent results in the theory of the Wiener number. Indian J. Chem. 32A, 651–661 (1993)
18.
Zurück zum Zitat Gutman, I., Furtula, B., (eds.): Distance in Molecular Graphs—Theory. Mathematical Chemistry Monographs, 12. University of Kragujevac and Faculty of Science Kragujevac, Kragujevac (2012) Gutman, I., Furtula, B., (eds.): Distance in Molecular Graphs—Theory. Mathematical Chemistry Monographs, 12. University of Kragujevac and Faculty of Science Kragujevac, Kragujevac (2012)
19.
Zurück zum Zitat Gutman, I., B. Furtula, B., (eds.): Distance in Molecular Graphs—Applications, Mathematical Chemistry Monographs, 13. University of Kragujevac and Faculty of Science Kragujevac, Kragujevac (2012) Gutman, I., B. Furtula, B., (eds.): Distance in Molecular Graphs—Applications, Mathematical Chemistry Monographs, 13. University of Kragujevac and Faculty of Science Kragujevac, Kragujevac (2012)
20.
21.
Zurück zum Zitat Nikolić, S., Trinajstić, N., Mihalić, Z.: The Wiener index: developments and applications. Croat. Chem. Acta 68, 105–129 (1995) Nikolić, S., Trinajstić, N., Mihalić, Z.: The Wiener index: developments and applications. Croat. Chem. Acta 68, 105–129 (1995)
22.
Zurück zum Zitat Polansky, O.E., Bonchev, D.: The Wiener number of graphs. I. General theory and changes due to some graph operations. MATCH Commun. Math. Comput. Chem. 21, 133–186 (1986) MathSciNetMATH Polansky, O.E., Bonchev, D.: The Wiener number of graphs. I. General theory and changes due to some graph operations. MATCH Commun. Math. Comput. Chem. 21, 133–186 (1986) MathSciNetMATH
23.
Zurück zum Zitat Rouvray, D.H.: Should we have designs on topological indices? In: King, R.B. (ed.) Chemical Application of Topology and Graph Theory, pp. 159–177. Elsevier, Amsterdam (1983) Rouvray, D.H.: Should we have designs on topological indices? In: King, R.B. (ed.) Chemical Application of Topology and Graph Theory, pp. 159–177. Elsevier, Amsterdam (1983)
24.
Zurück zum Zitat Rouvray, D.H.: The modeling of chemical phenomena using topological indices. J. Comput. Chem. 8, 470–480 (1987) MathSciNetCrossRef Rouvray, D.H.: The modeling of chemical phenomena using topological indices. J. Comput. Chem. 8, 470–480 (1987) MathSciNetCrossRef
25.
Zurück zum Zitat Todeschini, R., Consonni, V.: Handbook of Molecular Descriptors. Wiley-VCH, Weinheim (2000) CrossRef Todeschini, R., Consonni, V.: Handbook of Molecular Descriptors. Wiley-VCH, Weinheim (2000) CrossRef
26.
Zurück zum Zitat Trinajstić, N.: Chemical Graph Theory. CRC Press, Boca Raton (1983, 1992) Trinajstić, N.: Chemical Graph Theory. CRC Press, Boca Raton (1983, 1992)
27.
Zurück zum Zitat Wiener, H.: Structural determination of paraffin boiling points. J. Am. Chem. Soc. 69, 17–20 (1947) CrossRef Wiener, H.: Structural determination of paraffin boiling points. J. Am. Chem. Soc. 69, 17–20 (1947) CrossRef
Metadaten
Titel
Wiener index of certain families of hexagonal chains
verfasst von
Andrey A. Dobrynin
Ehsan Estaji
Publikationsdatum
07.03.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2019
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-018-1177-9

Weitere Artikel der Ausgabe 1-2/2019

Journal of Applied Mathematics and Computing 1-2/2019 Zur Ausgabe

Premium Partner