در موردشاخص های حسابی-هندسی نانو لوله های تک جداره حالت زیگ-زاگ

نویسندگان

1 گروه ریاضی، دانشکده ریاضی و کامپیوتر خوانسار، اصفهان

2 گروه ریاضی محض، دانشکده ریاضی، دانشگاه تربیت مدرس، تهران

چکیده

شاخص های توپولوژیکی کاربردهای بسیاری در مطالعات QSAR/QSPR دارند و امکان پیش بینی خواص فیزیکی-شیمیایی بسیاری از ساختارهای شیمیایی را بر اساس تجزیه تحلیل آماری معتبر با استفاده از یک مجموعه داده‌های کوچک فراهم می‌کنند. در مورد نانو اختارها محاسبه اکثر این شاخص ها که اولین قدم در به‌کارگیری آن‌هاست، معمولاً بقدری مشکل است که خود به موضوع اصلی مقالات تبدیل می‌شود و توجهی به کاربرد یا ارتباط آن‌ها با شاخص های ساده‌تر نمی‌شود. در این نوشتار به بررسی شاخص های حسابی-هندسی و تعمیم‌های آن‌ها در ارتباط با نانولوله‌ تک جداره حالت زیگ-زاگ TUHC_6 2p,q پرداخته و نشان می‌دهیم مقدار این خانواده از اندیس‌ها تقریباً با تعداد یال‌های گراف مولکولی آن‌ها برابرند، لذا ازلحاظ محاسبه ارزش چندانی ندارند. در عوض نسخه یالی شاخص های توپولوژیک مبتنی بر فاصله به‌عنوان جایگزین پیشنهاد می‌گردند و ارتباط برخی از معروف‌ترین آن‌ها با انرژی کل مولکول TUHC_6 2p,q مورد بررسی قرار می‌گیرد.

کلیدواژه‌ها


عنوان مقاله [English]

On geometric-arithmetic indices of single-walled zig-zag nanotubes

نویسندگان [English]

  • M . Eliasi 1
  • A. Iranmanesh 2
1 Department of mathematics, Khansar Faculty of Mathematics and Computer Science, Isfahan
2 Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University
چکیده [English]

Topological indices have significant applications in QSAR/QSPR studies, which allow the prediction of physical ad chemical properties for many chemical structures based on statically validated analysis starting from a small data set. With regard to nano structures, the problem is that the calculation of an index, which is the first step towards its application, usually is an immensely complicated subject. Consequently, computing the value of the index, will be the central issue rather than considering its application or comparing with other easy-computing indices. In this paper, the arithmetic-geometric indices and their generalizations in relation to the single-walled zig-zag nanotubes TUHC_6 2p, q have been investigated. Our results proved that the values of these families of indices are approximately equal to the number of the edges of their molecular graphs. From this point of view, the computation of such indices, for single-walled Zig-Zag nanotubes, is worthless. Instead, an edge version of distance-based topological indices has been purposed. We found and compared relationships between some of these new indices and the total energy of TUHC_6 2p, q nanotubes.

کلیدواژه‌ها [English]

  • Topological index
  • Single-walled zig-zag nanotube
  • Aarithmetic-geometric indices
  • Total energy
  • Molocular graph
[1] M. Endo, S. Iijima, M. S. Dresselhaus (Eds.),
“Carbon nanotubes,” Pergamon, 1996.
[2] M. Meyyappan, “Carbon Nanotubes: Science
and Applications,” CRC Press, Boca Raton, 2004.
[3] S. Iijima, T. Ichihashi, “Single-Shell Carbon
Nanotubes of 1-nm Diameter,” Nature, 363, 603-
605, 1993.
[4] S. Iijima, “Carbon nanotubes: past, present, and
future,” Physica B, 323, 1–5, 2002.
[5] T. Yamamoto, K. Watanabe, E. R. Hernandez,
“Mechanical properties, thermal stability and heat
transport in carbon nanotubes RID G-8978-2011
RID B-1285-2008,” Carbon Nanotubes: Advanced
Topics in the Synthesis, Structure, Properties and
Applications, 111, 165–194, 2008.
[6] P. Avouris, R. Martel, “Progress in carbon
nanotube electronics and photonics,” MRS
BULLETIN, 35, 306–313, 2010.
39 پاییز ۱۳۹8 |شماره سوم | سال ششم
[7] M. Dehmer, K. Varmuza, D. Bonchev,
“Statistical modelling of molecular descriptors in
QSAR/QSPR,” Volume 2 atthias;Varmuza, Kurt -
John Wiley, 2012.
[8] K. Roy, S. Kar, R.N. Das, “A primer on
QSAR/QSPR modeling: Fundamental Concepts,”
New York, Springer-Verlag, 2015.
[9] H. Timmerman, R. Todeschini ,V. Consonni, R.
Mannhold , H. Kubinyi, “Handbook of Molecular
Descriptors,” Weinheim, Wiley-VCH, 2002.
[10] J. Devillers, A. T. Balaban, “Topological
indices and related descriptors in QSAR and
QSPR,” Gordon and Breach Science Publishers,
Singapore. 1999.
[11] P. E. John, M. V. Diudea, “Wiener index of
zig-zag Polyhex nanotubes,” CROATICA
CHEMICA ACTA, 77, 127-132, 2004.
[12] M. V. Diudea, C. L. Nagy, “Periodic
nanostructures,” Springer, Dordrecht, 2007.
[13] M. Eliasi, B. Taeri, “Szeged and Balaban
indices of zigzag polyhex nanotoubes,” MATCH
Commun. Math. Comput. Chem., 56, 383‐402,
2006.
[14] M. Eliasi, B. Taeri, “Balaban index of zigzag
polyhex nanotorus,” J. Compute. Theor. Nanosci.,
4, 1174‐1178, 2006.
[15] A. Heydari, “Hyper Wiener index of C4C8(S)
nanotubes,” Curr. Nanosci. 6(2), 137–140, 2010.
[16] A. R. Ashrafi, F. Cataldo, A. Iranmanesh, O.
Ori (Eds.), “Topological modelling of
nanostructures and extended systems,” Springer,
2013.
[17] A. Taherpour, “Quantitative relationship
study of mechanical structure properties of empty
fullerenes,” Fullerenes, Nanotubes, and Carbon
Nanostructures, 16, 196–205, 2008.
[18] A. Taherpour, E. Mohammadinasab,
“Topological relationship between wiener,
Padmaker-Ivan, and Szeged indices and energy and
electric moments in armchair polyhex nanotubes
with the same circumference and varying lengths,”
Fullerenes, Nanotubes, and Carbon Nanostructures,
18(1), 72–88, 2010.
[19] M. Eliasi, “Topological indices and total
energy of zig-zag polyhex nanotubes,” Current
Nanoscience, 9, 502 – 513, 2013.
[20] D. Vukicevic, B. Furtula, “Topological index
based on the ratios of geometrical and arithmetical
means of end–vertex degrees of edges,” J. Math.
Chem. 46, 1369–1376, 2009.
[21] K. C. Das, I. Gutman, B. Furtula, “Survey on
geometric-arithmetic indices of graphs,” MATCH
Commun. Math. Comput. Chem., 65, 595-644,
2011.
[22] K. C. Das, N. Trinajstić, “Comparison
between geometric-arithmetic indices,” Croat.
Chim. Acta, 85, 353-357, 2012.
[23] A. Graovac, M. Ghorbani, M. A.
Hosseinzadeh, “Computing fifth geometricarithmetic index for nanostar dendrimers,” J. Math.
Nanosci. 1, 33-42, 2011.
[24] P. Wilczek, “new geometric-arithmetic
indices,” MATCH Commun. Math. Comput.
Chem., 79, 5-54, 2018.
[25] S. Moradi, S. Baba-Rahim, “Two types of
geometric-arithmetic indices of nanotubes and
nanotori,” MATCH Commun. Math. Comput.
Chem., 69, 165-174, 2013.
40 پاییز ۱۳۹8 |شماره سوم | سال ششم
[26] S. Chen, W. Liu, “The Geometric-Arithmetic
Index of Nanotubes,” Journal of Computational
and Theoretical Nanoscience, 7, 1993–1995, 2010.
[27] N. Soleimani, M. J. Nikmehr, H. Agha
Tavallaee, “Computation of the different
topological indices of nanostructures,” J. Natn. Sci.
Foundation Sri Lanka, 43 (2), 127 – 133, 2015.
[28] M. R. Farahani, “Some connectivity indices
and zagreb index of polyhex nanotubes,” Acta
Chim Slov. 59(4), 779-83, 2012.
[29] H. Wiener, “Structural determination of
paraffin boiling points,” J. Am. Chem. Soc., 69,
17-20, 1947.
[30] D. J. Klein, I. Lukovits, I. Gutman, “On the
definition of the hyper-Wiener index for cyclecontaining structures,” J. Chem. Inf. Comput. Sci.
35, 50-52, 1995.
[31] H. P. Schultz, “Topological Organic
Chemistry. 1. Graph Theory and Topological
Indices of Alkanes,” J. Chem. Inf. Comput. Sci.
29, 227-228, 1989.
[32] D. Plavsic, S. Nikolic, N. Trinajstic, Z.
Mihalic, “On the Harary index for the
characterization of chemical graphs,” J. Math.
Chem. 22, 235-250, 1993.
[33] D. Janezic, A. Milicevic, S. Nikolić, N.
Trinajstic, “Graph theoretical matrices in
chemistry,” in: Mathematical Chemistry
Monographs, vol. 3, University of Kragujevac,
Kragujevac, 3, (a) p. 62-64, (b) p. 79-80, (c) p.
80-81, 2007.
[34] A. T. Balaban, D. Mills, O. Ivanciuc, S. C.
Basak, “Reverse Wiener indices,” Croat. Chem.
Acta, 73(4), 923-941, 2000.
[35] M. Eliasi, B. Taeri, “Distance in zig-zag
polyhex nanotubes,” Current Nanoscience, 5(4),
514-518, 2009.
[36] A. T. Balaban, “Highly discriminating
distance based numerical descriptor,” Chem. Phys.
Lett. 89, 399-404, 1982.
[37] M. Knora, R. Skrekovski, A. Tepeh,
“Mathematical aspects of Balaban index,”
MATCH Commun. Math. Comput. Chem., 79,
685-716, 2018.
[38] I. Gutman, “A formula for the Wiener number
of trees and its extension to graphs containing
cycles,” Graph Theory Notes, 27, 9-15, 1994.
[39] P. V. Khadikar, S. Karmarkar, V. K. Agrawal,
J. Singh, A. Shrivastava, I. Lukovits, M. V.
Diudea, “Szeged index-Applications for drug
modelling,” Lett. Drug. Des. Discov, 2, 606-624,
2005.