Wiener and detour indices of a new type of nanostar dendrimers

A. Karbasioun, Ali Reza Ashrafi

Abstract


The Wiener and detour indices of a molecular graph G are defined as the sum of the lengths of all shortest and longest paths between the vertices of G. In this paper the exact formulae for the Wiener and detour indices of a new type of nanostar dendrimers are given.


Keywords


nanostar dendrimer; molecular graph; Wiener index, detour index

Full Text:

PDF

References


H. Hosoya, Topological Index. A Newly Proposed Quantity Characterizing the Topological Nature of Structural Isomers of Saturated Hydrocarbons, Bull. Chem. Soc. Japan, 44, 2332–2339 (1971).

H. Wiener, Structural Determination of Paraffin Boiling Points, J. Am. Chem. Soc., 69, 17–20 (1947).

MOLE db – Molecular Descriptors Data Base, Milano Chemometrics and QSAR Research Group, http://michem.disat.unimib.it/mole_db.

R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, WILEY – VCH, Weinheim, 2000.

F. Harary, Graph Theory, Addison-Wesley, Reading, Massachusetts, 1969.

D. Amić, N. Trinajstić, On the Detour Matrix, Croat. Chem. Acta, 68, 53–62 (1995).

I. Lukovits, The Detour Index, Croat. Chem. Acta, 69, 873–882 (1996).

N. Trinajstić, S. Nikolić, Z. Mihalić, On Computing the Molecular Detour Matrix, Int. J. Quantum Chem., 65, 415–419 (1997).

N. Trinajstić, S. Nikolić, B. Lučić, D. Amić and Z. Mihalić, The Detour Matrix in Chemistry, J: Chem. Inf. Comput. Sci., 37, 631–638 (1997).

D. Janežič, A. Miličević, S. Nikolić and N. Trinajstić, Graph-Theoretical Matrices in Chemistry, University of Kragujevac, Kragujevac, 2007.

P. E. John, Ueber die Berechnung des Wiener-Index fuer ausgewaehlte Delta-dimensionale Gitterstrukturen, MATCH Comm. Math. Comp. Chem., 32, 207–219 (1995).

M. V. Diudea, A. Graovac, Generation and graphtheoretical properties of C4-tori, MATCH Commun. Math. Comput. Chem., 44, 93–102 (2001).

M. V. Diudea, I. Silaghi-Dumitrescu, B. Parv, Toranes versus torenes, MATCH Commun. Math. Comput. Chem., 44, 117–133 (2001).

M.V. Diudea, P.E. John, Covering polyhedral tori, MATCH Commun. Math. Comput. Chem., 44, 103–116 (2001).

M. V. Diudea, Toroidal Graphenes from 4-Valent Tori, Bull. Chem. Soc. Jpn., 75, 487–492 (2002).

M. V. Diudea, Hosoya Polynomial in Tori, MATCH Commun. Math. Comput. Chem., 45, 109–122 (2002).

P. E. John, M. V. Diudea, Wiener index of zig-zag polyhex nanotubes, Croat. Chem. Acta, 77, 127–132 (2004).

M.V. Diudea, M. Stefu, B. Parv, P. E. John, Wiener index of armchair polyhex nanotubes, Croat. Chem. Acta,, 77, 111–115 (2004).

D. Vukičević, N. Trinajstić, Wiener indices of benzenoid graphs, Bull. Chemist & Technoligist Macedonia, 23, 113–129 (2004).

Ivan Gutman, Slavko Radenkovic, A simple formula for calculating resonance energy of benzenoid hydrocarbons, Bulletin of the Chemists and Technologists of Macedonia, 25, 17–21 (2006).

S. Yousefi, A. R. Ashrafi, An exact expression for the Wiener index of a polyhex nanotorus, MATCH Commun. Math. Comput. Chem., 56, 169–178 (2006).

S. Yousefi, A. R. Ashrafi, An algorithm for constructing Wiener matrix of TUC4C8(R) nanotubes, Current Nanoscience, 4, 161–165 (2008).

A. R. Ashrafi, S. Yousefi, Computing the Wiener Index of a TUC4C8(S) Nanotorus, MATCH Commun Math Comput Chem, 57, 403–410 (2007).

S. Yousefi, A. R. Ashrafi, An Exact Expression for the Wiener Index of a TUC4C8(R) Nanotorus, J Math Chem, 42, 1031–1039 (2007).

A. R. Ashrafi, S. Yousefi, A New Algorithm for Computing Distance Matrix and Wiener Index of Zig-zag Polyhex Nanotubes Nanoscale Res Lett, 2, 202–206 (2007).

L. Xu, H. Deng, The Schultz Molecular Topological Index of C4C8 Nanotubes, MATCH Commun. Math. Comput. Chem., 59, 421–428 (2008).

S. Chen, Q. Jang, Y. Hou, The Wiener and Schultz Index of Nanotubes Covered by C4, MATCH Commun. Math. Comput. Chem., 59, 429–435 (2008).

M. Eliasi, B. Taeri, Szeged Index of Armchair Polyhex Nanotubes, MATCH Commun. Math. Comput. Chem., 59, 437–450 (2008).

H. Yousefi-Azari, A. R. Ashrafi, A. Bahrami, J. Yazdani, Computing Topological Indices of Some Types of Benzenoid Systems and Nanostars, Asian J. Chem., 20, 15-20 (2008).

A. R. Ashrafi, M. Mirzargar, PI, Szeged and edge Szeged indices of an infinite family of nanostar dendrimers, Indian Journal of Chemistry, 47A, 538-541 (2008).




DOI: http://dx.doi.org/10.20450/mjcce.2009.221

Refbacks

  • There are currently no refbacks.




Copyright (c) 2016 A. Karbasioun, Ali Reza Ashrafi

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.