Skip to main content
Erschienen in: Journal of Applied Mathematics and Computing 1-2/2018

11.01.2018 | Original Research

Graphs having extremal monotonic topological indices with bounded vertex k-partiteness

verfasst von: Fang Gao, Duo-Duo Zhao, Xiao-Xin Li, Jia-Bao Liu

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The vertex k-partiteness \(v_k(G)\) of graph G is defined as the fewest number of vertices whose deletion from G yields a k-partite graph. In this paper, we introduce some monotonic topological indices, and characterize the extremal corresponding graphs among graphs of order n and fixed vertex k-partiteness.

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 Alizadeh, Y., Iranmanesh, A., Dos̆lić, T.: Additively weighted Harary index of some composite graphs. Discrete Math. 313, 26–34 (2013)MathSciNetCrossRefMATH Alizadeh, Y., Iranmanesh, A., Dos̆lić, T.: Additively weighted Harary index of some composite graphs. Discrete Math. 313, 26–34 (2013)MathSciNetCrossRefMATH
2.
Zurück zum Zitat Ashrafi, A.R., Saheli, M., Ghorbani, M.: The eccentric connectivity index of nanotubes and nanotori. J. Comput. Appl. Math. 235, 4561–4566 (2011)MathSciNetCrossRefMATH Ashrafi, A.R., Saheli, M., Ghorbani, M.: The eccentric connectivity index of nanotubes and nanotori. J. Comput. Appl. Math. 235, 4561–4566 (2011)MathSciNetCrossRefMATH
3.
Zurück zum Zitat Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. Macmillan and Elsevier, London and New York (1976)CrossRefMATH Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. Macmillan and Elsevier, London and New York (1976)CrossRefMATH
4.
Zurück zum Zitat de Freitas, M.A.A., Gutman, I., Robbiano, M.: Graphs with maximum Laplacian-energy-like invariant and incidence energy. MATCH Commun. Math. Comput. Chem. 75, 331–342 (2016)MathSciNetMATH de Freitas, M.A.A., Gutman, I., Robbiano, M.: Graphs with maximum Laplacian-energy-like invariant and incidence energy. MATCH Commun. Math. Comput. Chem. 75, 331–342 (2016)MathSciNetMATH
5.
Zurück zum Zitat Fallat, S., Fan, Y.Z.: Bipartiteness and the least eigenvalue of signless Laplacian of graphs. Linear Algebra Appl. 436, 3254–3267 (2012)MathSciNetCrossRefMATH Fallat, S., Fan, Y.Z.: Bipartiteness and the least eigenvalue of signless Laplacian of graphs. Linear Algebra Appl. 436, 3254–3267 (2012)MathSciNetCrossRefMATH
6.
Zurück zum Zitat Furtula, B., Gutman, I., Dehmer, M.: On structure-sensitivity of degree-based topological indices. Appl. Math. Comput. 219, 8973–8978 (2013)MathSciNetMATH Furtula, B., Gutman, I., Dehmer, M.: On structure-sensitivity of degree-based topological indices. Appl. Math. Comput. 219, 8973–8978 (2013)MathSciNetMATH
7.
Zurück zum Zitat Gupta, S., Singh, M., Madan, A.K.: Connective eccentricity index: a novel topological descriptor for predicting biological activity. J. Mol. Graph. Model. 18, 18–25 (2000)CrossRef Gupta, S., Singh, M., Madan, A.K.: Connective eccentricity index: a novel topological descriptor for predicting biological activity. J. Mol. Graph. Model. 18, 18–25 (2000)CrossRef
8.
Zurück zum Zitat Gupta, S., Singh, M., Madan, A.K.: Application of graph theory: relationship of eccentric connectivity index and Wiener’s index with anti-inflammatory activity. J. Math. Anal. Appl. 266, 259–268 (2002)MathSciNetCrossRefMATH Gupta, S., Singh, M., Madan, A.K.: Application of graph theory: relationship of eccentric connectivity index and Wiener’s index with anti-inflammatory activity. J. Math. Anal. Appl. 266, 259–268 (2002)MathSciNetCrossRefMATH
9.
Zurück zum Zitat Gutman, I., Rus̆c̆ić, B., Trinajstić, N., Wilcox, C.F.: Graph theory and molecular orbitals. J. Chem. Phys. 62, 3390–3405 (1975)CrossRef Gutman, I., Rus̆c̆ić, B., Trinajstić, N., Wilcox, C.F.: Graph theory and molecular orbitals. J. Chem. Phys. 62, 3390–3405 (1975)CrossRef
10.
Zurück zum Zitat Gutman, I., Trinajstić, N.: Graph theory and molecular orbitals. Total $\pi $-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17, 535–538 (1972)CrossRef Gutman, I., Trinajstić, N.: Graph theory and molecular orbitals. Total $\pi $-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17, 535–538 (1972)CrossRef
11.
Zurück zum Zitat Gutman, I.: Degree-based topological indices. Croat. Chem. 86, 351–361 (2013)CrossRef Gutman, I.: Degree-based topological indices. Croat. Chem. 86, 351–361 (2013)CrossRef
12.
Zurück zum Zitat Gutman, I., Medina, L.C., Pizarro, P., Robbiano, M.: Graphs with maximum Laplacian and signless Laplacian Estrada index. Discrete Appl. Math. 339, 2664–2671 (2016)MathSciNetMATH Gutman, I., Medina, L.C., Pizarro, P., Robbiano, M.: Graphs with maximum Laplacian and signless Laplacian Estrada index. Discrete Appl. Math. 339, 2664–2671 (2016)MathSciNetMATH
13.
Zurück zum Zitat Gutman, I., Tos̆ović, J.: Testing the quality of molecular structure descriptors VertexCdegree-based topological indices. J. Serb. Chem. Soc. 78, 805–810 (2013)CrossRef Gutman, I., Tos̆ović, J.: Testing the quality of molecular structure descriptors VertexCdegree-based topological indices. J. Serb. Chem. Soc. 78, 805–810 (2013)CrossRef
14.
15.
Zurück zum Zitat Li, H.S., Li, S.C., Zhang, H.H.: On the maximal connective eccentricity index of bipartite graphs with some given parameters. J. Math. Anal. Appl. 454, 453–467 (2017)MathSciNetCrossRefMATH Li, H.S., Li, S.C., Zhang, H.H.: On the maximal connective eccentricity index of bipartite graphs with some given parameters. J. Math. Anal. Appl. 454, 453–467 (2017)MathSciNetCrossRefMATH
16.
Zurück zum Zitat Liu, J.B., Pan, X.F.: Minimizing Kirchhoff index among graphs with a given vertex bipartiteness. Appl. Math. Comput. 291, 84–88 (2016)MathSciNet Liu, J.B., Pan, X.F.: Minimizing Kirchhoff index among graphs with a given vertex bipartiteness. Appl. Math. Comput. 291, 84–88 (2016)MathSciNet
17.
Zurück zum Zitat Nihat, A., Das, K.C., Çevik, A.S.: Some properties on the tensor product of graphs obtained by monogenic semigroups. Appl. Math. Comput. 235, 352–357 (2014)MathSciNetMATH Nihat, A., Das, K.C., Çevik, A.S.: Some properties on the tensor product of graphs obtained by monogenic semigroups. Appl. Math. Comput. 235, 352–357 (2014)MathSciNetMATH
18.
Zurück zum Zitat Plavs̆ić, D., Nikolić, S., Trinajstić, N., Mihalić, Z.: On the Harary index for the characterization of chemical graphs. J. Math. Chem. 12, 235–250 (1993)MathSciNetCrossRef Plavs̆ić, D., Nikolić, S., Trinajstić, N., Mihalić, Z.: On the Harary index for the characterization of chemical graphs. J. Math. Chem. 12, 235–250 (1993)MathSciNetCrossRef
19.
Zurück zum Zitat Robbiano, M., Morales, K.T., San Martín, B.: Extremal graphs with bounded vertex bipartiteness number. Linear Algebra Appl. 493, 28–36 (2016)MathSciNetCrossRefMATH Robbiano, M., Morales, K.T., San Martín, B.: Extremal graphs with bounded vertex bipartiteness number. Linear Algebra Appl. 493, 28–36 (2016)MathSciNetCrossRefMATH
20.
Zurück zum Zitat Sardana, S., Madan, A.K.: Predicting anti-HIV activity of TIBO derivatives: a computational approach using a novel topological descriptor. Mol. Model 8, 258–265 (2002)CrossRef Sardana, S., Madan, A.K.: Predicting anti-HIV activity of TIBO derivatives: a computational approach using a novel topological descriptor. Mol. Model 8, 258–265 (2002)CrossRef
21.
Zurück zum Zitat Todeschini, R., Conaoni, V.: New local vertex invariants and molecular descriptors based on funtions of the vertex degrees. Math. Comput. 64, 359–372 (2010) Todeschini, R., Conaoni, V.: New local vertex invariants and molecular descriptors based on funtions of the vertex degrees. Math. Comput. 64, 359–372 (2010)
22.
Zurück zum Zitat Wiener, H.: Structural determination of paraffin boiling point. J. Am. Chem. Soc. 69, 17–20 (1947)CrossRef Wiener, H.: Structural determination of paraffin boiling point. J. Am. Chem. Soc. 69, 17–20 (1947)CrossRef
23.
Zurück zum Zitat Xu, K., Das, K.C., Trinajstić, N.: The Harary Index of a Graph. Springer, Heidelberg (2015)CrossRefMATH Xu, K., Das, K.C., Trinajstić, N.: The Harary Index of a Graph. Springer, Heidelberg (2015)CrossRefMATH
24.
Zurück zum Zitat Xu, K., Liu, M.H., Das, K.C., Gutman, I., Furtula, B.: A survey on graphs extremal with respect to distance-based topological indices. Math. Comput. Chem. 71, 461–508 (2014)MathSciNetMATH Xu, K., Liu, M.H., Das, K.C., Gutman, I., Furtula, B.: A survey on graphs extremal with respect to distance-based topological indices. Math. Comput. Chem. 71, 461–508 (2014)MathSciNetMATH
25.
Zurück zum Zitat Xu, K., Das, K.C., Liu, H.: Some extremal results on the connective eccentricity index of graphs. J. Math. Anal. Appl. 433, 803–817 (2016)MathSciNetCrossRefMATH Xu, K., Das, K.C., Liu, H.: Some extremal results on the connective eccentricity index of graphs. J. Math. Anal. Appl. 433, 803–817 (2016)MathSciNetCrossRefMATH
Metadaten
Titel
Graphs having extremal monotonic topological indices with bounded vertex k-partiteness
verfasst von
Fang Gao
Duo-Duo Zhao
Xiao-Xin Li
Jia-Bao Liu
Publikationsdatum
11.01.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2018
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-017-1151-y

Weitere Artikel der Ausgabe 1-2/2018

Journal of Applied Mathematics and Computing 1-2/2018 Zur Ausgabe