Zagreb Topological Properties of Hexa Organic Molecular Structures

Page: [226 - 238] Pages: 13

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Abstract

Background: In connection with the study of chemical graph theory, it has been explored that a single number can capture the numerical representation of a molecular structure, and this number is known as a topological property (index).

Objective: This study aimed to explore a few Zagreb topological properties for four hexa organic molecular structures (hexagonal, honeycomb, silicate, and oxide) based on the valency and valency sum of atoms in the structure.

Methods: We employed the technique of partitioning the set of bonds according to the valency and valency-sum of end atoms of each bond and then performed the computation by using combinatorial rules of counting (that is, the rule of sum and the rule of product). The obtained results were also compared numerically and graphically.

Results and Conclusion: Exact values of five valencies based and five valency-sum-based Zagreb topological properties were found for the underline chemical structures.

[1]
Consonni, T. V. Handbook of molecular descriptors. Wiley-VCH: Weinheim, 2000.
[2]
Chartrand, G.; Zhang, P. Itroduction to graph theory. Tata McGraw-Hill Companies Inc: New York, 2006.
[3]
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]
[4]
Randić, M. Characterization of molecular branching. J. Am. Chem. Soc., 1975, 97(23), 6609-6615.
[http://dx.doi.org/10.1021/ja00856a001]
[5]
Gutman, I.; Trinajstić, N. Graph theory and molecular orbitals. total φ-electron energy of alternant hydrocarbons. Chem. Phys. Lett., 1972, 17(4), 535-538.
[http://dx.doi.org/10.1016/0009-2614(72)85099-1]
[6]
Furtula, B.; Graovac, A.; Vukičević, D. Augmented zagreb index. J. Math. Chem., 2010, 48(2), 370-380.
[http://dx.doi.org/10.1007/s10910-010-9677-3]
[7]
Ghorbani, M.; Hosseinzadeh, M.A. The third version of zagreb index. Discrete Math. Algorithms Appl., 2013, 5(4), 1350039.
[http://dx.doi.org/10.1142/S1793830913500390]
[8]
Mahalank, P.; Majhi, B.K.; Delen, S.; Cangul, I.N. Zagreb indices of square snake graphs. Montes Taurus J. Pure Appl. Math., 2021, 3(3), 165-171.
[9]
Mondal, S.; Dey, A.; De, N.; Pal, A. QSPR analysis of some novel neighbourhood degree-based topological descriptors. Complex Intelligent Syst., 2021, 7(2), 977-996.
[http://dx.doi.org/10.1007/s40747-020-00262-0]
[10]
Mondal, S.; De, N.; Pal, A. On some general neighborhood degree based indices. Int. J. Appl. Math., 2020, 32(6), 1037-1049.
[http://dx.doi.org/10.12732/ijam.v32i6.10]
[11]
Mondal, S.; De, N.; Pal, A. On some new neighborhood degree-based indices for someoxide and silicate networks. J. Multidisci. Scienti., 2019, 2(3), 384-409.
[12]
A, V.; S, M.; De, N.; Pal, A. Topological properties of bismuth triiodide using neighborhood m-polynomial. I. J. Mathe. Trends .Tech., 2019, 67(10), 83-90.
[http://dx.doi.org/10.14445/22315373/IJMTT-V65I10P512]
[13]
Shirdel, G.H.; Rezapour, H.; Sayadi, A.M. The hyper zagreb index of graph operations. Iranian J. Math. Chem., 2013, 4(2), 213-220.
[14]
Dhanalakshmi, K.; Jerline, J.A.; Raj, L.B.M. Modified zagreb index of some chemical structure trees. Int. J. Math. Appl., 2017, 5(1), 285-290.
[15]
Ranjini, P.S.; Lokesha, V.; Usha, A. Relation between phenylene and hexagonal squeeze using harmonic index. Int. J. Graph Theory, 2013, 1(4), 116-121.
[16]
Shanmukha, M.C.; Basavarajappa, N.S.; Usha, A.; Shilpa, K.C. Novel neighbourhood redefined first and second zagreb indices on carborundum structures. J. Appl. Math. Comput., 2021, 66(1-2), 263-276.
[http://dx.doi.org/10.1007/s12190-020-01435-3]
[17]
Salman, M.; Ali, F.; Khalid, I.; Ur Rehman, Masood Some valency oriented molecular invariants of certain networks. Comb. Chem. High Throughput Screen., 2022, 25(3), 462-475.
[http://dx.doi.org/10.2174/1386207323666201020145239] [PMID: 33081681]