IJPAM: Volume 115, No. 4 (2017)

Title

COMPUTING SANSKRUTI INDEX OF
V-PHENYLENIC NANOTUBES AND NANOTORI

Authors

H. Jiang$^1$, M.S. Sardar$^2$, M.R. Farahani$^3$,
M. Rezaei$^4$, M.K. Siddiqui$^5$
$^1$School of Information Science and Engineering
Chengdu University
Chengdu, 610106, P.R. CHINA
$^2$University of Management and Technology (UMT)
Lahore, PAKISTAN
$^3$Department of Applied Mathematics
Iran University of Science and Technology (IUST)
Narmak, Tehran, 16844, IRAN
$^4$Department of Mathematics
Buein Zahra Technical University
Buein Zahra, Qazvin, IRAN
Department of Mathematics
$^5$Comsats Institute of Information Technology
Sahiwal, PAKISTAN

Abstract

Among topological descriptors connectivity topological indices are very important and they have a prominent role in chemistry. One of them is Sanskruti index defined as $S(G)=\sum_{uv \in E(G)} (\frac{S_uS_v}{S_u+S_v-2})^3$ where $S_u$ is the summation of degrees of all neighbors of vertex $u$ in $G$. In this paper we compute this topological index for V-phenylenic nanotube and nanotori.

History

Received: May 4, 2017
Revised: July 10, 2017
Published: August 10, 2017

AMS Classification, Key Words

AMS Subject Classification: 05C90, 05C35, 05C12
Key Words and Phrases: molecular graph, benzenoid, Capra operation, topological index, Sanskruti index

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Bibliography

1
R. TODESCHINI AND V. CONSONNI: Handbook of Molecular Descriptors, Wiley-TUACH, Weinheim (2000).

2
N. TRINAJSTIC: Chemical Graph Theory, 2nd ed. CRC Press; Boca Raton, FL: (1992); 20-75.

3
I. GUTMAN, N. TRINAJSTIC: Graph theory and molecular orbitals. Total f-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17(4), (1972), 535-538. https://doi.org/10.1016/0009-2614(72)85099-1

4
P. J. CAMERON: Cambridge University Press, Cambridge, (1994).

5
M. V. DIUDEA: Fuller. Nanotub. Carbon Nanostruct, (2002), 10, 273-292.

6
M. RANDIC: Characterization of molecular branching. J. Amer. Chem. Soc. 97, (1975) 6609-6615. DOI: 10.1021/ja00856a001

7
S. M. HOSAMANI: S. M. HOSAMANI: Computing Sanskruti index of certain nanostructures. Journal of Applied Mathematics and Computing. In press, 2017. DOI 10.1007/s12190-016-1016-9.

8
M.S. SARDAR, S. ZAFAR, M.R. FARAHANI. Computing Sanskruti index of the Polycyclic Aromatic Hydrocarbons. Geology, Ecology, and Landscapes. In press, (2017), $https://dx.doi.org/10.1080/24749508.2017.1301056$

9
Y.Y. GAO, M.R. FARAHANI, M.S. SARDAR, S. ZAFAR. On the Sanskruti Index of Circumcoronene Series of Benzenoid. Applied Mathematics. 8 (4), (2017), 520-524. doi:10.4236/am.2017.84041

10
Y.Y. GAO, M.S. SARDAR, S.M. HOSAMANI, M.R. FARAHANI. Computing sanskruti index of $TURC_4C_8(s)$ nanotube. International Journal of Pharmaceutical Sciences and Research. 8 (10), (2017), 1000-03. doi: 10.13040/IJPSR.0975-8232.8(10).1000-03.

11
Y.Y. GAO, M.S. SARDAR, S. ZAFAR, M.R. FARAHANI. Computing Sanskruti index of dendrimer nanostars. International Journal of Pure and Applied Mathematics. 115(2), In press, (2017), $https://ijpam.eu/contents/index.php$

12
V. ALAMIAN, A. BAHRAMI AND B. EDALATZADEH: PI Polynomial of V-Phenylenic Nanotubes and Nanotori. Int. J. Mol. Sci., 9(3), (2008), 229-234; doi:10.3390/ijms9030229

13
M. ALAEIYAN, A. BAHRAMI AND M. R. FARAHANI: Cyclically Domination Polynomial of Molecular Graph of Some Nanotubes. Digest. J. Nanomater. Bios. 6(1), (2011), 143-147.

14
J. ASADPOUR: Some topological polynomial indices of nanostructures, Optoelectron. Adv. Mater.-Rapid Commun. 5(7), (2011), 769-772.

15
A. BAHRAMI AND J. YAZDANI: Vertex PI Index of V-Phenylenic Nanotubes and Nanotori. Digest Journal of Nanomaterials and Biostructures, 4(1), (2009), 141-144.

16
M. DAVOUDI MOHFARED, A. BAHRAMI AND J. YAZDANI: PI Polynomial of V-Phenylenic Nanotubes. Digest Journal of Nanomaterials and Biostructures, 5(2), (2010), 441-445.

17
M. R. FARAHANI: Computing $GA_5$ index of V-Phenylenic Nanotubes and Nanotori. Int. J. Chem Model. 5(4), (2013), 479-484.

18
M. R. FARAHANI: Computing fourth atom-bond connectivity index of V-Phenylenic Nanotubes and Nanotori. Acta Chimica Slovenica. 60(2), (2013), 429-432.

19
M. R. FARAHANI: omputing Theta Polynomial and Theta Index of V-phenylenic Planar, Nanotubes and Nanotoris. Int. J. Theoretical Chemistry. 1(1), (2013), 01-09.

20
M.R. FARAHANI, M.R. RAJESH KANNA: The Generalized Zagreb Index of V-Phenylenic Nanotubes and Nanotorus. Journal of Chemical and Pharmaceutical Research. 7(11), (2015), 241-245.

21
M. GHORBANI, H. MESGARANI, S. SHAKERANEH: Computing GA index and ABC index of V-phenylenic nanotube. Optoelectron. Adv. Mater.-Rapid Commun. 5(3), (2011), 324-326.

22
A. D. MANIKPURI, S. AZIZ, E. JOHN, P.V. KHADIKAR: Computation of the Sadhana (Sd) Index of Linear Phenylenes and Corresponding Hexagonal Sequences. Iranian J. Math. Chem, 1(1), (2010), 79-90.

23
P.E. JOHN, S. AZIZ, P.V. KHADIKAR: Use of Structure Codes (Counts) for Computing Topological Indices of Carbon Nanotubes: Sadhana (Sd) Index of Phenylenes and its Hexagonal Squeezes. Iranian J. Math. Chem, 1(1), (2010), 91-94.

24
Z. YARAHMADI: A Note on the First Geometric-Arithmetic Index of Hexagonal Systems and Phenylenes. Iranian J. Math. Chem, 2(2), (2011), 101-108.

25
S. MORADI, S. BABARAHIMI AND M. GHORBANI: Two Types of Geometric-Arithmetic index of V-phenylenic Nanotube. Iranian J. Math. Chem, 2(2), (2011), 109-117.

26
M. GHORBANI, H. MESGARANI, S. SHAKERANEH: Optoelectron. Adv. Mater. Rapid Commun. 2011, 5(3), 324-326.

27
N. PRABHAKARA RAO AND K. L. LAKSHMI: Eccentricity Connectivity Index of V-Phenylenic Nanotubes. Digest Journal of Nanomaterials and Biostructures, 6(1), (2010), 81-87.

28
S.C. BASAK, Q. ZHU AND D. MILLS: Prediction of Anticancer Activity of 2-phenylindoles: Comparative Molecular Field Analysis Versus Ridge Regression using Mathematical Molecular Descriptors. Acta Chim. Slov. 57, (2010), 541-550.

29
S. J. CYVIN AND I. GUTMAN: Lecture Note in Chemistry, Springer-Verlag, Berlin, (1988), 46.

30
I. GUTMAN AND S. J. CYVIN: The number of Kekul, structures in long benzenoid chains. J. Chem. Phys. 1988, 147(1), 121-125. https://doi.org/10.1016/0009-2614(88)80235-5

31
I. GUTMAN AND S. J. CYVIN: Counting Kekule structures in some conjugated systems with repeating units. J. Serb. Chem. Soc. 1990, 55, 555-561.

32
I. GUTMAN, S. MARKOVIC, V. LUKOVIC, V. RADIVOJEVIC AND S. RANDI´C Coll. Sci. Papers Fac. Sci. Kragujevac, (1987), 8, 15-34.

33
I. GUTMAN, P. PETKOVIC AND P. V. KHADIKAR: Bounds for the total $\pi$-electron energy of phenylenes. Revue Roumaine de Chimie. 41, (1996), 637-643.

How to Cite?

DOI: 10.12732/ijpam.v115i4.19 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 4
Pages: 859 - 865


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