TOPOLOGICAL INDICES IN HYPERTUBES OF HYPERCUBES
Keywords:
graph, topological index, n-cube, hyper-tube, hyper-torus, n-dimensional spaceAbstract
A topological index is a single number descriptor that characterizes the molecular graph topology up to isomorphism. Hyper-tubes, open or closed, consisting of hyper-cubes of n-dimensions have been designed and formulas for some topological indices, counting vary substructures or characteristics, were established.
References
L. Schläfli, “Theorie der vielfachen Kontinuität Zürcher und Furrer”, Zürich, 1901 (Reprinted in: Ludwig Schläfli, 1814-1895, “Gesammelte Mathematische Abhandlungen”, Verlag Birkhäuser, Basel, 1950, Band 1).
http://en.wikipedia.org/wiki/Convex_hull; http://en.wikipedia.org/wiki/Simplex; http://en.wikipedia.org/wiki/Cross-polytope; http://en.wikipedia.org/wiki/Hypercube. (accessed 12.05.2015)
H.S.M. Coxeter, “Regular Polytopes”, 3rd ed. New York: Dover, 1973.
B. Grünbaum, “Convex Polytopes”, Graduate Texts in Mathematics (2nd ed.), Springer, 2003.
L. Euler, Novi Comm. Acad. Scient. Imp. Petrop., 1758, 4, 109.
M.V. Diudea, “Multi-shell polyhedral clusters”, Springer, 2016 (in preparation).
C.L. Nagy, M.V. Diudea, MATCH Commun. Math. Comput. Chem., 2016 (in press).
A. Parvan-Moldovan, M. V. Diudea, Iran. J. Math. Chem., 2015, 6, 163.
M.V. Diudea, Bull. Chem. Soc. Japan, 2002, 75, 487.
F. Harary, “Graph Theory”, Addison–Wesley, Reading, MA, 1969.
M.V. Diudea, “Nanomolecules and Nanostructures - Polynomials and Indices”, MCM, No. 10, Univ. Kragujevac, 2010.
P.E. John, A.E. Vizitiu, S. Cigher, M.V. Diudea, MATCH Commun. Math. Comput. Chem., 2007, 57, 479.
D.Ž. Djoković, Combin. J. Theory Ser. B, 1973, 14, 263.
P.M. Winkler, Discrete Appl. Math., 1984, 8, 209.
M.V. Diudea, S. Klavžar, Acta Chem. Sloven., 2010, 57, 565.
M.V. Diudea, Carpath. J. Math., 2006, 22, 43.
M.V. Diudea, S. Cigherand, P.E. John, MATCH, Commun. Math. Comput. Chem. 2008, 60, 237.
M.V. Diudea, S. Cigher and A.E. Vizitiu, M.S. Florescu, P.E. John, J. Math. Chem., 2009, 45, 316.
M.V. Diudea, in: Gutman I., Furtula B., (Eds) “Novel Molecular Structure Descriptors-Theory and Applications I”, Univ Kragujevac, Kragujevac, 2010, 191.
M.V. Diudea in: Gutman I., Furtula B., (Eds) “Novel Molecular Structure Descriptors-Theory and Applications II”, Univ Kragujevac, Kragujevac, 2010b, 57.
I. Gutman, S. Klavžar, J. Chem. Inf. Comput. Sci., 1995, 35, 1011.
M.V. Diudea, S. Cigher, P.E. John, MATCH Commun. Math. Comput. Chem., 2008, 60, 237.
M.V. Diudea, S. Klavžar, Acta Chem. Sloven., 2010, 57, 565.
M.V. Diudea, A.E. Vizitiu, D. Janežič, J. Chem. Inf. Model., 2007, 47, 864.
M.V. Diudea, J. Math. Chem., 2009, 45, 295.
M.V. Diudea, N. Dorosti, A. Iranmanesh, Carpath. J. Math., 2010, 4, 247.
P.V. Khadikar, Nat. Acad. Sci. Lett., 2000, 23, 113.
M.H. Khalifeh, H. Yousefi-Azari, A.R. Ashrafi, Discrete Appl. Math., 2008, 156, 1780.
A.R. Ashrafi, M. Ghorbani, M. Jalali, J. Theor. Comput. Chem., 2008, 7, 221.
T. Mansour, M. Schork, Discr. Appl. Math., 2009, 157, 1600.
M.V. Diudea, A. Ilić, M. Ghorbani, A.R. Ashrafi, Croat. Chem. Acta, 2010, 83, 283.
M.V. Diudea, J. Chem. Inf. Comput. Sci., 1997, 37, 300.
M.H. Khalifeh, H. Yousefi-Azari, A.R. Ashrafi, Linear Algebra Appl., 2008, 429, 2702.
C.L. Nagy, M.V. Diudea, NANO–Studio, Babes-Bolyai Univ., Cluj, 2009.
https://oeis.org/, The On-Line Encyclopedia of Integer Sequences” (accessed 12.05. 2015).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2016 Studia Universitatis Babeș-Bolyai Chemia
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
