Edge Corona Product And Its Topological Descriptors with Applications in Complex Molecular Structures

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, Riphah International University Lahore, Pakistan

2 Punjab School Education Department, Govt Higher Secondary School Nangal Sahdan Muridke 39000, Sheikhupura, Pakistan

3 Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan

4 Faculty of Arts and Science, Department of Mathematics, Bursa Uludag University, Gorukle 16059 Bursa, Turkey

Abstract

Graph operations offer a robust framework that enables the analysis, modeling, and resolution of intricate problems. Their versatility and broad range of applications make them essential across numerous fields of study and research, playing an irreplaceable role in tackling complex challenges. A topological index is a real number associated with a graph that gives insight into the topological properties of the graph. There are numerous topological indices in this era now, with three variants like degree based, distance based and eccentricity based topological indices. In this paper, we studied a well known graph operation named as edge corona product and investigate their some degree based topological indices. As applications, this graph operations can be used to study topological properties of complex structure of linear and cyclic silicate networks, together with triangular and double triangular networks. Some existing results in the literature can be obtained as corollaries of the new results. A conjecture is proposed relating the general first Zagreb index of the edge corona product of two graphs.

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References

[1] I.R. Abdolhosseinzadeh, F. Rahbarnia, and M. Tavakoli, Some indices of edge corona of two graphs, Appl. Math. E-Notes 18 (2018), no. 1, 13–24.
[2] S. Akhter, Z. Iqbal, A. Aslam, and W. Gao, Computation of Mostar index for some graph operations, Int. J. Quantum Chem. 121 (2021), no. 15, Article ID: e26674.
https://doi.org/10.1002/qua.26674
[3] A. Alameri, N. Al-Naggar, M. Al-Rumaima, and M. Alsharafi, Y-index of some graph operations, Int. J. Appl. Eng. Res. 15 (2020), no. 2, 173–179.
[4] H. Ali, H.M.A. Siddiqui, and M.K. Shafiq, On degree-based topological descriptors of oxide and silicate molecular structures, MAGNT Res. Rep. 4 (2016), 135–142.
[5] M. Arezoomand and B. Taeri, Zagreb indices of the generalized hierarchical product of graphs, MATCH Commun. Math. Comput. Chem. 69 (2013), no. 1, 131–140.
[6] A.R. Ashrafi, T. Došlić, and A. Hamzeh, The Zagreb coindices of graph operations, Discrete Appl. Math. 158 (2010), no. 15, 1571–1578.
https://doi.org/10.1016/j.dam.2010.05.017
[7] N. Biggs, E.K. Lloyd, and R.J. Wilson, Graph Theory, Clarendon Press, 1986.
[8] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, American Elsevier Publishing Company, 1976.
[9] S. Brezovnik, N. Tratnik, and P.Ž. Pleteršek, Weighted Wiener indices of molecular graphs with application to alkenes and alkadienes, Mathematics 9 (2021), no. 2, Article ID: 153.
https://doi.org/10.3390/math9020153
[10] K.C. Das, A. Yurttas, M. Togan, A.S. Cevik, and I.N. Cangul, The multiplicative Zagreb indices of graph operations, J. Inequal. Appl. 2013 (2013), no. 1, Article number 90.
https://doi.org/10.1186/1029-242X-2013-90
[11] N. De, Computing F-index of different Corona products of graphs, Bull. Math. Sci. Appl. 19 (2017), 24–30.
[12] S. Delen and I.N. Cangul, A new graph invariant, Turkish J Anal. Number Theory 6 (2018), no. 1, 30–33.
https://doi.org/10.12691/tjant-6-1-4
[13] S. Delen and I.N. Cangul, Extremal problems on components and loops in graphs, Acta Math. Sin. Engl. Ser. 35 (2019), no. 2, 161–171.
https://doi.org/10.1007/s10114-018-8086-6
[14] R. Diestel, Graph Theory, Springer, Berlin, 2017.
[15] M. Eliasi and B. Taeri, Four new sums of graphs and their wiener indices, Discrete Appl. Math. 157 (2009), no. 4, 794–803.
https://doi.org/10.1016/j.dam.2008.07.001
[16] L. R. Foulds, Graph Theory Applications, Springer, New York, 2012.
[17] B. Furtula, I. Gutman, Ž.K. Vukićević, G. Lekishvili, and G. Popivoda, On an old/new degree–based topological index, Bulletin Classe des Sciences mathematiques et natturalles (2015), no. 40, 19–32.
[18] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535–538.
https://doi.org/10.1016/0009-2614(72)85099-1
[19] S. Hayat and M. Imran, Computation of topological indices of certain networks, Appl. Math. Comput. 240 (2014), 213–228.
https://doi.org/10.1016/j.amc.2014.04.091
[20] A. Ilić, G. Yu, and L. Feng, On the eccentric distance sum of graphs, J. Math. Anal. Appl. 381 (2011), no. 2, 590–600.
https://doi.org/10.1016/j.jmaa.2011.02.086
[21] M.K. Jamil, Distance-based topological indices and double graph, Iran. J. Math. Chem. 8 (2017), no. 1, 83–91.
https://doi.org/10.22052/ijmc.2017.43073
[22] A. Khaksari and M. Ghorbani, On the forgotten topological index, Iran. J. Math. Chem. 8 (2017), no. 3, 327–33.8
https://doi.org/10.22052/ijmc.2017.43481
[23] M.H. Khalifeh, H. Yousefi-Azari, and A.R. Ashrafi, The hyper-Wiener index of graph operations, Comput. Math. Appl. 56 (2008), no. 5, 1402–1407.
https://doi.org/10.1016/j.camwa.2008.03.003
[24] M.H. Khalifeh, H. Yousefi-Azari, and A.R. Ashrafi, The first and second Zagreb indices of some graph operations, Discrete Appl. Math. 157 (2009), no. 4, 804–811.
https://doi.org/10.1016/j.dam.2008.06.015
[25] P. Manuel and I. Rajasingh, Topological properties of silicate networks, 2009 5th IEEE GCC Conference and Exhibition, IEEE, 2009, pp. 1–5
https://doi.org/10.1109/IEEEGCC.2009.5734286
[26] A. Miličević, S. Nikolić, and N. Trinajstić, On reformulated Zagreb indices, Mol. Divers. 8 (2004), no. 4, 393–399.
https://doi.org/10.1023/B:MODI.0000047504.14261.2a
[27] K. Pattabiraman, S. Nagarajan, and M. Chendrasekharan, Zagreb indices and coindices of product graphs, J. Prime Res. Math. 10 (2015), 80–91.
[28] A. Prathik, K. Uma, and J. Anuradha, An overview of application of graph theory, Int. J. Chemtech Res. 9 (2016), no. 2, 242–248.
[29] G. Shirdel, H. Rezapor, and A. Sayadi, The hyper-Zagreb index of graph operations, Iran. J. Math. Chem. 4 (2013), no. 2, 213–220.
https://doi.org/10.22052/ijmc.2013.5294
[30] S. Ulagammal, J.V. Vivin, and I.N. Cangul, On star coloring of degree splitting of cartesian product graphs, Jordan J. Math. Stat. 15 (2022), no. 2, 243– 254.
[31] V. Yegnanarayanan, P.R. Thiripurasundari, and T. Padmavathy, On some graph operations and related applications, Electron. Notes Discrete Math. 33 (2009), 123–130.
https://doi.org/10.1016/j.endm.2009.03.018
 
Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 10 June 2024

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