Identyfikatory
Języki publikacji
Abstrakty
Singly and doubly vertex-weighted Wiener polynomials are generalizations of both vertex-weighted Wiener numbers and the ordinary Wiener polynomial. In this paper, we show how the vertex-weighted Wiener polynomials of a graph change with subdivision operators, and apply our results to obtain vertex-weighted Wiener numbers.
Czasopismo
Rocznik
Tom
Strony
5--23
Opis fizyczny
Bibliogr. 28 poz., rys.
Twórcy
autor
- Department of Mathematics Kazerun Branch, Islamic Azad University P. O. Box: 73135-168, Kazerun, Iran
autor
- Tarbiat Modares University Faculty of Mathematical Sciences Department of Pure Mathematics P.O. Box: 14115-137, Tehran, Iran
autor
- University of Zagreb Faculty of Civil Engineering Kaciceva 26, 10000 Zagreb, Croatia
Bibliografia
- [1] Y. Alizadeh, A. Iranmanesh, T. Doslić, M. Azari, The edge Wiener index of suspensions, bottlenecks, and thorny graphs, Glas. Mat. Ser. Ill 49 (2014) 1, 1-12.
- [2] V. Andova, N. Cohen, R. Skrekovski, A note on Zagreb indices inequality for trees and unicyclic graphs, Ars Math. Contemp. 5 (2012) 1, 73-76.
- [3] M. Azari, Sharp lower bounds on the Narumi-Katayama index of graph operations, Appl. Math. Comput. 239 (2014), 409-421.
- [4] M. Azari, A. Iranmanesh, Chemical graphs constructed from, rooted product and their Zagreb indices, MATCH Commun. Math. Comput. Chem. 70 (2013) 3, 901-919.
- [5] M. Azari, A. Iranmanesh, Computation of the edge Wiener indices of the sum of graphs, Ars Combin. 100 (2011), 113-128.
- [6] M. Azari, A. Iranmanesh, Computing the eccentric-distance sum for graph operations, Discrete Appl. Math. 161 (2013) 18, 2827-2840.
- [7] F. Cataldo, O. Ori, A. Graovac, Wiener index of 1-pentagon fulle.re.nic infinite lattice, Int. J. Chem. Model. 2 (2010), 165-180.
- [8] M.R. Darafsheh, M.H. Khalifeh, Calculation of the Wiener, Szeged, and PI indices of a certain nanostar dendrimer, Ars Combin. 100 (2011), 289-298.
- [9] M.V. Diudea, QSPR/QSAR studies by molecular descriptors, NOVA, New York, 2001.
- [10] M.V. Diudea, Wiener index of de.ndrime.rs, MATCH Commun. Math. Comput. Chem. 32 (1995), 71-83.
- [11] T. Doslić, Vertex-weighted Wiener polynomials for composite graphs, Ars Math. Contemp. 1 (2008), 66-80.
- [12] B. Furtula, I. Gutman, H. Lin, More trees with all degrees odd having extremal Wiener index, MATCH Commun. Math. Comput. Chem. 70 (2013), 293-296.
- [13] I. Gutman, An exceptional property of first Zagreb index, MATCH Commun. Math. Comput. Chem. 72 (2014), 733-740.
- [14] I. Gutman, A property of the Wiener number and its modifications, Indian J. Chem. 36 (1997) A, 128-132.
- [15] I. Gutman, Degree-based topological indices, Croat. Chem. Acta. 86 (2013), 351-361.
- [16] I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. Total tt— electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535-538.
- [17] H. Hosoya, On some counting polynomials in chemistry, Discrete Appl. Math. 19 (1988), 239-257.
- [18] M.H. Khalifeh, H. Yousefi-Azari, A.R. Ashrafi, The hyper-Wiener index of graph operations, Comput. Math. Appl. 56 (2008) 5, 1402-1407.
- [19] D.J. Klein, T. Doslić, D. Bonchev, Vertex-weightings for distance-moments and thorny graphs, Discrete Appl. Math. 155 (2007), 2294-2302.
- [20] R. Nasiri, H. Yousefi-Azari, M.R. Darafsheh, A.R. Ashrafi, Remarks on the Wiener index of unicyclic graphs, J. Appl. Math. Comput. 41 (2013), 49-59.
- [21] T. Reti, On the relationships between the first and second Zagreb indices, MATCH Commun. Math. Comput. Chem. 68 (2012), 169-188.
- [22] T. Reti, I. Gutman, Relations between ordinary and multiplicative Zagreb indices, Bull. Inter. Math. Virtual Inst. 2 (2012), 133-140.
- [23] B.E. Sagan, Y.N. Yeh, P. Zhang, The Wiener polynomial of a graph, Inter. J. Quantum Chem. 60 (1996) 5, 959-969.
- [24] J. Sedlar, D. Vukicevic, F. Cataldo, O. Ori, A. Graovac, Compression ratio of Wiener-index in 2D^-rectangular and polygonal lattices, Ars Math. Contemp. 7 (2014) 1, 1-12.
- [25] D. Stevanovic, Hosoya polynomials of composite graphs, Discrete Math. 235 (2001), 237-244.
- [26] N. Trinajstić, Chemical graph theory, CRC Press, Boca Raton, FL, 1992.
- [27] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947), 17-20.
- [28] W. Yan, B.Y. Yang, Y.N. Yeh, The behavior of Wiener indices and polynomials of graphs under five graph decorations, Appl. Math. Lett. 20 (2007), 290-295.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Identyfikator YADDA
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