Topological indices of Kragujevac trees

• Cruz, Roberto ^[1] ; Gutman, Iván ^[2] ; Rada, Juan ^[1]
  1. [1] Universidad de Antioquia

     Universidad de Antioquia

     Colombia

     
  2. [2] University of Kragujevac

     University of Kragujevac

     Opština Kragujevac, Serbia

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 33, Nº. 4, 2014, págs. 471-482
• Idioma: inglés
• DOI: 10.4067/S0716-09172014000400008
• Enlaces
  • Texto completo
• Resumen

  • We find the extremal values of the energy, the Wiener index and several vertex-degree-based topological indices over the set of Kragujevac trees with the central vertex of fixed degree.

• Referencias bibliográficas
  • Citas [1] C. A. Coulson, On the calculation of the energy in unsaturated hydrocarbon molecules, Proc. Cambridge Phil. Soc., 36, pp. 201-203,...
  • [2] A. A. Dobrynin, R. Entriguer and I. Gutman, Wiener index of trees:‏ Theory and applications, Acta Appl. Math, 66, pp. 211-249, (2001).‏
  • [3] E. Estrada, L. Torres, L. Rodríguez and I. Gutman, An atom-bond‏ connectivity index: Modelling the enthalpy of formation of alkanes,‏...
  • [4] B. Furtula, A. Graovac and D. Vukicevic, Augmented Zagreb index,‏ J. Math. Chem., 48, pp. 370-380, (2010).‏
  • [5] B. Furtula, I. Gutman and M. Dehmer, On structure-sensitivity of‏ degree-based topological indices, Appl. Math. Comput., 219, pp. 8973-8978,...
  • [6] B. Furtula, I. Gutman, M. Ivanovic and D. Vukicevic, Computer search‏ for trees with minimal ABC index, Appl. Math. Comput., 219, pp....
  • [7] I. Gutman, Acyclic systems with extremal Huckel π-electron energy,‏ Theor. Chim. Acta, 45, pp. 79-87, (1977).‏
  • [8] I. Gutman, Degree-based topological indices, Croat. Chem. Acta, 86,‏ pp. 351-361, (2013).‏
  • [9] I. Gutman, The energy of a graph, Ber. Math.-Statist. Sekt.‏ Forschungsz. Graz, 103, pp. 1-22, (1978).‏
  • [10] I. Gutman, Topology and stability of conjugated hydrocarbons. The‏ dependence of total π-electron energy on molecular topology, J. Serb.‏...
  • [11] I. Gutman and B. Furtula, Trees with smallest atom-bond connectivity‏ index, MATCH Commun. Math. Comput. Chem., 68, pp. 131-136,‏ (2012).‏
  • [12] I. Gutman, B. Furtula and M. Ivanovic, Notes on trees with minimal atom-bond connectivity index, MATCH Commun. Math. Comput. Chem., 67,...
  • [13] I. Gutman and N. Trinajstic, Graph theory and molecular orbitals.‏ Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett.,‏...
  • [14] B. Horoldagva and I. Gutman, On some vertex-degree-based graph‏ invariants, MATCH Commun. Math. Comput. Chem., 65, pp. 723-730, (2011).‏
  • [15] S. A. Hosseini, M. B. Ahmadi and I. Gutman, Kragujevac Trees with‏ minimal Atom-Bond Connectivity Index, MATCH Commun. Math.‏ Comput....
  • [16] X. Li, Y. Shi and I. Gutman, Graph Energy, Springer, New York,‏ (2012).‏
  • [17] M. Randic, On characterization of molecular branching, J. Am. Chem.‏ Soc., 97, pp. 6609-6615, (1975).‏
  • [18] A. Schwenk, Computing the characteristic polynomial of a graph, in:‏ Lectures Notes in Mathematics, vol 406, Springer-Verlag, Berlin,...
  • [19] D. Vukicevic and B. Furtula, Topological index based on the ratios of‏ geometrical and arithmetical means of end-vertex degrees of edges,...
  • [20] H. Wiener, Structural determination of paraffin boiling points, J.‏ Amer. Chem. Soc., 69, pp. 17-20, (1947).‏
  • [21] B. Zhou and N. Trinajstic, On a novel connectivity index, J. Math.‏ Chem., 46, pp. 1252-1270, (2009).‏
  • [22] L. Zhong, The harmonic index for graphs,Appl. Math. Lett., 25, pp. 561-566, (2012).