Generic placeholder image

Combinatorial Chemistry & High Throughput Screening

Editor-in-Chief

ISSN (Print): 1386-2073
ISSN (Online): 1875-5402

Research Article

Some Valency Oriented Molecular Invariants of Certain Networks

Author(s): Muhammad Salman, Faisal Ali, Masood Ur Rehman* and Imran Khalid

Volume 25, Issue 3, 2022

Published on: 20 October, 2020

Page: [462 - 475] Pages: 14

DOI: 10.2174/1386207323666201020145239

Price: $65

Abstract

Background: The valency of an atom in a molecular structure is the number of its neighboring atoms. A large number of valency based molecular invariants have been conceived, which correlate certain physio-chemical properties like boiling point, stability, strain energy and many more chemical compounds.

Objective: Our aim is to study the valency based molecular invariants for four hexa chemical structures, namely hexagonal network, honeycomb network, oxide network and silicate sheet network.

Methods: We use the technique of atom-bonds partition according to the valences of atoms to find results.

Results and Conclusion: Exact values of valency-based molecular invariants, namely the Randi index, atom bond connectivity index, geometric arithmetic index, harmonic index, Zagreb indices, Zagreb polynomials, F-index and F-polynomial, are found for four hexa chemical structures.

Keywords: Valency, Randić index, harmonic index, ABC index, GA index, Zagreb index, forgotten index, network

Graphical Abstract

[1]
Chartrand, G.; Zhang, P. Itroduction to graph theory; Tata McGraw-Hill Companies Inc: New York, 2006.
[2]
Rucker, G.; Rucker, C. On topological indices, boiling points, and cycloalkanes. J. Chem. Inf. Comput. Sci., 1999, 39, 788-802.
[http://dx.doi.org/10.1021/ci9900175]
[3]
Ahmad, A. On the degree based topological indices of benzene ring embedded in P-type surface in 2D network. Hacet. J. Math. Stat., 2018, 47, 9-18.
[4]
Siddiqui, M.K.; Naeem, M.; Rahman, N.A.; Imran, M. Computing topological indices of certain networks. J. Optoelectron. Adv. Mater., 2016, 18, 884-892.
[5]
Dobrynin, A.A.; Entringer, R.; Gutman, I. Wiener index of trees: Theory and applications. Acta Appl. Math., 2001, 66, 211-249.
[http://dx.doi.org/10.1023/A:1010767517079]
[6]
Imran, M.; Siddiqui, M.K.; Naeem, M.; Iqbal, M.A. On topological properties of symmetric chemical structures. Symmetry (Basel), 2018, 10(5), 173.
[7]
Mirzargar, M.; Ashrafi, A.R. Some distance-based topological indices of a non-commuting graph. Hacet. J. Math. Stat., 2012, 41(4), 515-526.
[8]
Wiener, H. Structural determination of paraffin boiling points. J. Am. Chem. Soc., 1947, 69(1), 17-20.
[http://dx.doi.org/10.1021/ja01193a005 PMID: 20291038]
[9]
Caporossi, G.; Gutman, I.; Hansen, P.; Pavlović, L. Graphs with maximum connectivity index. Comput. Biol. Chem., 2003, 27, 85-90.
[http://dx.doi.org/10.1016/S0097-8485(02)00016-5]
[10]
Graovac, A.; Ghorbani, M.; Hosseinzadeh, M.A. Computing fifth goemetric-arithmetic index for nanostar dendrimers. J. Math. Nanosci., 2011, 1, 33-42.
[11]
Graovac, A.; Hosseinzadeh, M.A. Computing ABC_4 index of nanostar dendrimers. Adv. Mater. Rapi Commun., 2010, 4, 1419-1422.
[12]
Gutman, I. Degree-based topological indices. Croat. Chem. Acta, 2013, 86(4), 351-361.
[13]
Hayata, S.; Imran, M. Computation of topological indices of certain networks. Appl. Math. Comput., 2014, 240, 213-228.
[http://dx.doi.org/10.1016/j.amc.2014.04.091]
[14]
Hu, Y.; Li, X.; Shi, Y.; Xu, T.; Gutman, I. On molecualr graphs with smallest and greatest zeroth-order general Randić index. MATCH. Commun. Math. Comput. Chem., 2005, 54, 425-434.
[http://dx.doi.org/10.3390/sym10050173]
[15]
Imran, M.; Hayat, S.; Malik, M.Y.H. On topological indices of certain interconnected networks. Appl. Math. Comput., 2014, 244, 936-951.
[http://dx.doi.org/10.1016/j.amc.2014.07.064]
[16]
Xu, K.; Liu, M.; Das, K.C.; Gutman, I.; Furtula, B. A survey on graphs extremal with respect to distance-based topological indices. MATCH Commun. Math. Comput. Chem., 2014, 71, 461-508.
[17]
Randić, M. On characterization of molecular branching. J. Am. Chem. Soc., 1975, 97, 6609-6615.
[http://dx.doi.org/10.1021/ja00856a001]
[18]
Bollobás, B.; Erdös, P. Graph of extremal weights. Ars Comb., 1998, 50, 225-233.
[19]
Amic, D.; Beslo, D.; Lucic, B.; Nikolic, S.; Trinajstić, N. The vertex-connectivity index revisited. J. Chem. Inf. Comput. Sci., 1998, 38, 819-822.
[http://dx.doi.org/10.1021/ci980039b]
[20]
Li, X.; Gutman, I. Mathematical aspects of Randić type molecular structure description., 2006.
[21]
Estrada, E.; Torres, L. Rodr”i” ́guez, L.; Gutman, I. An atom-bond connectivity index: Modelling the enthalpy of formation of alkanes. Indian J. Chem., 1998, 37A, 849-855.
[http://dx.doi.org/10.5562/cca2294]
[22]
Vukičević, D.; Furtula, B. Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges. J. Math. Chem., 2009, 46, 1369-1376.
[http://dx.doi.org/10.1007/s10910-009-9520-x]
[23]
Fajtlowicz, S. On conjectures of Grafitti II. Congr. Numer., 1987, 60, 189-197.
[24]
Gutman, I.; Trinajstić, N. Graph theory and molecular orbitals, total π-electron energy of alternant hydrocarbans. Chem. Phys. Lett., 1972, 17, 535-538.
[25]
Gutman, I.; Das, K.C. Some properties of the second Zagreb index. MATCH Commun. Math. Comput. Chem., 2004, 50, 103-112.
[http://dx.doi.org/10.1016/0009-2614(72)85099-1]
[26]
Furtula, B.; Gutman, I. A forgotten topological index. J. Math. Chem., 2015, 53, 1184-1190.
[http://dx.doi.org/10.1007/s10910-015-0480-z]]
[27]
Hussain, Z.; Munir, M.; Rafique, S.; Kang, S.M. Topological characterizations and index analysis of new degree-based descriptors of honeycomb networks. Symmetry (Basel), 2018, 10, 478.
[http://dx.doi.org/10.3390/sym10100478]

Rights & Permissions Print Cite
© 2024 Bentham Science Publishers | Privacy Policy