Topological indices of Kragujevac trees
DOI:
https://doi.org/10.4067/S0716-09172014000400008Keywords:
Topological indices, Kragujevac trees, índices topológicos, árboles de Kragujevac.Abstract
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.References
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[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, Indian J. Chem., 37A, pp. 849-855, (1998).
[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, (2013).
[6] B. Furtula, I. Gutman, M. Ivanovic and D. Vukicevic, Computer search for trees with minimal ABC index, Appl. Math. Comput., 219, pp. 767-772, (2012).
[7] I. Gutman, Acyclic systems with extremal Huckel ð-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 ð-electron energy on molecular topology, J. Serb. Chem. Soc., 70, pp. 441-456, (2005).
[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, pp. 467-482, (2012).
[13] I. Gutman and N. Trinajstic, Graph theory and molecular orbitals. Total ð-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, pp. 535-538, (1972).
[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. Chem., 71, pp. 5-20, (2014).
[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, Heidelberg, pp. 153-172, (1974).
[19] D. Vukicevic and B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem., 46, pp. 1369-1376, (2009).
[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).
[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, Indian J. Chem., 37A, pp. 849-855, (1998).
[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, (2013).
[6] B. Furtula, I. Gutman, M. Ivanovic and D. Vukicevic, Computer search for trees with minimal ABC index, Appl. Math. Comput., 219, pp. 767-772, (2012).
[7] I. Gutman, Acyclic systems with extremal Huckel ð-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 ð-electron energy on molecular topology, J. Serb. Chem. Soc., 70, pp. 441-456, (2005).
[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, pp. 467-482, (2012).
[13] I. Gutman and N. Trinajstic, Graph theory and molecular orbitals. Total ð-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, pp. 535-538, (1972).
[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. Chem., 71, pp. 5-20, (2014).
[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, Heidelberg, pp. 153-172, (1974).
[19] D. Vukicevic and B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem., 46, pp. 1369-1376, (2009).
[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).
Published
2017-03-23
How to Cite
[1]
R. Cruz, I. Gutman, and J. Rada, “Topological indices of Kragujevac trees”, Proyecciones (Antofagasta, On line), vol. 33, no. 4, pp. 471-482, Mar. 2017.
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