Computation of reverse degree-based topological indices of hex-derived networks

Ali N. A. Koam; Ali Ahmad; Yasir Ahmad; Ali N. A. Koam; Ali Ahmad; Yasir Ahmad

doi:10.3934/math.2021658

AIMS Mathematics

2021, Volume 6, Issue 10: 11330-11345. doi: 10.3934/math.2021658

Previous Article Next Article

Research article

Computation of reverse degree-based topological indices of hex-derived networks

1.
Department of Mathematics, College of Science, Jazan University, New Campus, Jazan 2097, Saudi Arabia
2.
College of Computer Science and Information Technology, Jazan University, Jazan, Saudi Arabia

Received: 18 May 2021 Accepted: 18 July 2021 Published: 05 August 2021
MSC : 05C90

Network theory gives an approach to show huge and complex frameworks through a complete arrangement of logical devices. A network is made is made of vertices and edges, where the degree of a vertex refers to the number of joined edges. The degree appropriation of a network represents the likelihood of every vertex having a particular degree and shows significant worldwide network properties. Network theory has applications in many disciplines like basic sciences, computer science, engineering, medical, business, public health and sociology. There are some important networks like logistical networks, gene regulatory networks, metabolic networks, social networks, derived networks. Topological index is a numerical number assigned to the molecular structure/netwrok which is used for correlation analysis in physical, theoretical and environmental chemistry. The hex-derived networks are created by hexagonal networks of dimension $ t $, these networks have an assortment of valuable applications in computer science, medical science and engineering. In this paper we discuss the reverse degree-based topological for third type of hex-derived networks.
- topological indices,
- reverse degree,
- hex-derived networks
Citation: Ali N. A. Koam, Ali Ahmad, Yasir Ahmad. Computation of reverse degree-based topological indices of hex-derived networks[J]. AIMS Mathematics, 2021, 6(10): 11330-11345. doi: 10.3934/math.2021658

Related Papers:

Abstract

Network theory gives an approach to show huge and complex frameworks through a complete arrangement of logical devices. A network is made is made of vertices and edges, where the degree of a vertex refers to the number of joined edges. The degree appropriation of a network represents the likelihood of every vertex having a particular degree and shows significant worldwide network properties. Network theory has applications in many disciplines like basic sciences, computer science, engineering, medical, business, public health and sociology. There are some important networks like logistical networks, gene regulatory networks, metabolic networks, social networks, derived networks. Topological index is a numerical number assigned to the molecular structure/netwrok which is used for correlation analysis in physical, theoretical and environmental chemistry. The hex-derived networks are created by hexagonal networks of dimension $ t $, these networks have an assortment of valuable applications in computer science, medical science and engineering. In this paper we discuss the reverse degree-based topological for third type of hex-derived networks.

References

[1]	M. Karelson, Molecular Descriptors in QSAR/QSPR, Wiley, New York, 2000.
[2]	A. Aslam, Y. Bashir, S. Ahmad, W. Gao, On Topological Indices of Certain Dendrimer Structures, Z. Naturforsch., 72 (2017), 559-566. doi: 10.1515/zna-2017-0081
[3]	M. Bača, J. Horváthová, M. Mokrišová, A. Suhányiová, On topological indices of fullerenes, Appl. Math. Comput., 251 (2015), 154-161.
[4]	A. Q. Baig, M. Imran, H. Ali, On topological indices of poly oxide, poly silicate, DOX and DSL networks, Canad. J. Chem., 93 (2015), 730-739. doi: 10.1139/cjc-2014-0490
[5]	S. Hayat, M. Imran, Computation of topological indices of certain networks, Appl. Math. Comput., 240 (2014), 213-228.
[6]	A. N. A. Koam, A. Ahmad, Polynomials of degree-based indices for three dimensional mesh network, Comput., Mater. Continua, 65 (2020), 1271-1282. doi: 10.32604/cmc.2020.011736
[7]	M. Javaid, J. B. Liu, M. A. Rehman, S. Wang, On the certain topological indices of Titania Nanotube $TiO_2[m, n]$, Z. Für Naturforsch. A, 72 (2017), 647-654.
[8]	G. Hong, Z. Gu, M. Javaid, H. M. Awais, M. K. Siddiqui, degree-based topological invariants of metal-organic networks, IEEE Access, 8 (2020), 68288-68300. doi: 10.1109/ACCESS.2020.2985729
[9]	Z. Iqbal, A. Aslam, M. Ishaq, M. Aamir, Characteristic study of irregularity measures of some nanotubes, Can. J. Phys., 97 (2019), 1125-1132. Available from: https://doi.org/10.1139/cjp-2018-0619.
[10]	V. R. Kulli, Reverse Zagreb and reverse hyper-Zagreb indices and their polynomials of rhombus silicate networks, Ann. Pure Appl. Math., 16 (2018), 47-51. doi: 10.22457/apam.v16n1a6
[11]	A. Ahmad, On the degree-based topological indices of benzene ring embedded in P-type-surface in 2D network, Hacet. J. Math. Stat., 47 (2018), 9-18.
[12]	M. Imran, A. Q. Baig, H. Ali, On molecular topological properties of hex-derived networks, J. Chemometr., 30 (2016), 121-129. doi: 10.1002/cem.2785
[13]	T. Vetrík, Polynomials of degree-based indices for hexagonal nanotubes, U.P.B. Sci. Bull., Series B, 81 (2019), 109-120.
[14]	M. Arockiaraj, S. R. J. Kavitha, S. Mushtaq, K. Balasubramanian, Relativistic topological molecular descriptors of metal trihalides, J. Mol. Struc., 1217 (2020), 128368. doi: 10.1016/j.molstruc.2020.128368
[15]	M. Arockiaraj, S. Klavžar, J. Clement, S. Mushtaq, K. Balasubramanian, Edge distance-based topological indices of strength-weighted graphs and their application to coronoid systems, carbon nanocones and $SiO_2$ nanostructures, Mol. Inf., (2019). Available from: https://doi.org/10.1002/minf.201900039.
[16]	M. Arockiaraj, J. Clement, D. Paul, K. Balasubramanian, Relativistic distance-based topological descriptors of Linde type A zeolites and their doped structures with very heavy elements, Mol. Phy., 119 (2021), e1798529. Available from: https://doi.org/10.1080/00268976.2020.1798529.
[17]	M. Randic, Characterization of molecular branching, J. Am. Chem. Soc., 97 (1975), 6609-6615. doi: 10.1021/ja00856a001
[18]	E. Estrada, L. Torres, L. Rodriguez, I. Gutman, An atom-bond connectivity index: Modelling the enthalpy of formation of alkanes, Indian J Chem., Sect. A, 37 (1998), 849-855.
[19]	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 (2009), 1369-1376. doi: 10.1007/s10910-009-9520-x
[20]	I. Gutman, K. C. Das, The first Zagreb index 30 years after, Match Commun. Math. Comput. Chem, 50 (2004), 83-92.
[21]	I. Gutman, N. Trinajstic, Graph theory and molecular orbitals, Total pi-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17 (1972), 535-538. doi: 10.1016/0009-2614(72)85099-1
[22]	G. H. Shirdel, H. Rezapour, A. M. Sayadi, The hyper-Zagreb index of graph operations, Iran. J. Math. Chem., 4 (2013), 213-220.
[23]	B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem., 53 (2015), 1184-1190. doi: 10.1007/s10910-015-0480-z
[24]	B. Furtula, A. Graovac, D. Vukicevic, Augmented zagreb index, J. Math. Chem., 48 (2010), 370-380.
[25]	P. S. Ranjini, V. Lokesha, A. Usha, Relation between phenylene and hexagonal squeeze using harmonic index, Int. J. Graph Theory, 1 (2013), 116-121.
[26]	D. Zhao, Y. M. Chu, M. K. Siddiqui, K. Ali, M. Nasir, M. T. Younas, et al. On reverse degree-based topological indices of polycyclic metal organic network, Polycycl. Aromat. Comp., 2021. Available from: https://doi.org/10.1080/10406638.2021.1891105.
[27]	A. Ahmad, Comparative study of $ve$-degree and $ev$-degree topological descriptors for benzene ring embedded in P-type-surface in 2D network, Polycycl. Aromat. Comp., (2020). Available from: https://doi.org/10.1080/10406638.2020.1834415.
[28]	J. Zhang, M. K. Siddiqui, A. Rauf, M. Ishtiaq, On $ve$-degree and $ev$-degree-based topological properties of single walled Titanium dioxide nanotube, J. Clust. Sci., (2020), Available from: https://doi.org/10.1007/s10876-020-01842-3.
[29]	N. Zahra, M. Ibrahim, M. K. Siddiqui, On topological indices for swapped networks modeled by optical transpose interconnection system, IEEE Access, 8 (2020), 200091-200099. Available from: 10.1109/ACCESS.2020.3034439.
[30]	Z. Raza, Leap Zagreb connection numbers for some networks models, Indones. J. Chem., 20 (2020), 1407-1413. doi: 10.22146/ijc.53393
[31]	M. K. Siddiqui, M. Imran, A. Ahmad, On Zagreb indices, Zagreb polynomials of some nanostar dendrimers, Appl. Math. Comput., 280 (2016), 132-139.
[32]	A. Aslam, S. Ahmad, W. Gao, On certain topological indices of Boron triangular nanotubes, Z. Naturforsch., 72 (2017), 711-716. doi: 10.1515/zna-2017-0135
[33]	M. Javaid, H. Zafar, Q. Zhu, A. M. Alanazi, Improved Lower Bound of LFMD with Applications of Prism-Related Networks, Mathematical Problems in Engineering, vol. 2021, Article ID: 9950310, Available from: https://doi.org/10.1155/2021/9950310.
[34]	J. B Liu, Z. Raza, M. Javaid, Zagreb Connection Numbers for Cellular Neural Networks, Discrete Dynamics in Nature and Society, vol. 2020, Article ID: 8038304. Available from: https://doi.org/10.1155/2020/8038304.
[35]	Eshrag A. Refaee, A. Ahmad, A Study of Hexagon Star Network with Vertex-Edge-Based Topological Descriptors, Complexity, vol. 2021, Article ID 9911308. Available from: https://doi.org/10.1155/2021/9911308.
[36]	M. S. Chen, K. G. Shin, D. D. Kandlur, Addressing, routing, and broadcasting in hexagonal mesh multiprocessors, IEEE Trans. Comput., 39 (1990), 10-18. doi: 10.1109/12.46277
[37]	F. Simonraj, A. George, On the Metric Dimension of $HDN_3$ and $PHDN_3$, In: Proceedings of the IEEE International Conference on Power, Control, Signals and Instrumentation Engineering (ICPCSI), Chennai, India, 21-22 September 2017, 1333-1336.
[38]	H. Ali, M. A. Binyamin, M. K. Shafiq, W. Gao, On the degree-based topological indices of some derived networks, Mathematics, 7 (2019), 612. doi: 10.3390/math7070612.
[39]	C. C Wei, H. Ali, M. A. Binyamin, M. N. Naeem, J. B Liu, Computing degree-based topological properties of third type of hex-derived networks, Mathematics, 7 (2019), 368. doi: 10.3390/math7040368
[40]	Ali N. A. Koam, A. Ahmad, M. F. Nadeem, Comparative study of valency-based topological descriptor for hexagon star network, Comput. Syst. Sci. Eng., 36 (2021), 293-306. doi: 10.32604/csse.2021.014896
[41]	H. Ali, A. Sajjad, On further results of hex derived networks, Open J. Discret. Appl. Math., 2 (2019), 32-40. doi: 10.30538/psrp-odam2019.0009
[42]	M. Imran, A. Q. Baig, S. U. Rehman, H. Ali, R. Hasni, Computing topological polynomials of mesh-derived networks, Discret. Math. Algorithms Appl., 10 (2018), 1850077. doi: 10.1142/S1793830918500775
[43]	P. Song, H. Ali, M. A. Binyamin, B. Ali, J. B. Liu, On Computation of Entropy of Hex-Derived Network, Hindawi, Complexity, 2021 (2021), Article ID 9993504, 18 pages. Available from: https://doi.org/10.1155/2021/9993504.
[44]	X. Zhao, H. Ali, B. Ali, M. A. Binyamin, J. B. Liu, A. Raza, Statistics and calculation of entropy of dominating David derived networks, Hindawi, Complexity, 2021 (2021), Article ID 9952481, 15 pages. Available from: https://doi.org/10.1155/2021/9952481.
[45]	M. Imran, A. Q. Baig, H. Ali, On topological properties of dominating David derived networks, Can. J. Chem., 94 (2015), 137-148.
[46]	A. Aslam, S. Ahmad, W. Gao, On certain topological indices of Boron triangular nanotubes, Z. Naturforsch., 72 (2017), 711-716. doi: 10.1515/zna-2017-0135

Reader Comments

Your name:*

Email:*
© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)