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Bounds on the Neighborhood Inverse Sum In-degree Index of Graphs with Applications to Benzenoid | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 02 آذر 1404 اصل مقاله (1.19 M) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30619.2555 | ||
| نویسندگان | ||
| Deepa Balasubramaniyan1؛ Natarajan Chidambaram1؛ Modjtaba Ghorbani* 2 | ||
| 1Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed to be University, Kumbakonam - 612 001, Tamil Nadu, India | ||
| 2Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran 16785-163, Iran | ||
| چکیده | ||
| The neighborhood inverse sum indeg index, denoted as $ISI_N(\mathcal{G})$, of a simple graph $\mathcal{G}$ is defined as the sum of the terms $( \frac{\mathscr{\delta}_{\mathcal{G}}(\mathscr{r})\mathscr{\delta}_{\mathcal{G}}(\mathscr{s})}{\mathscr{\delta}_{\mathcal{G}}(\mathscr{r})+\mathscr{\delta}_{\mathcal{G}}(\mathscr{s})} \) for all edges \( \mathscr{\mathscr{rs}} )$ in $\mathcal{G}$. Here, \( \mathscr{\delta}_{\mathcal{G}}(\mathscr{r}) \) represents the neighborhood degree of a vertex \( \mathscr{r} \), which is the sum of the degrees of the neighbours of \( \mathscr{r} \) in \( \mathcal{G} \). This article establishes bounds for the \( ISI_N(\mathcal{G}) \) index in relation to various graph invariants and its connection to neighborhood degree-sum-based topological indices. We also present results on the \( ISI_N \) index concerning different graph operations. Furthermore, we analyze the physico-chemical properties of 55 benzenoid hydrocarbons and validate our model with 10 more benzenoid hydrocarbons. | ||
| کلیدواژهها | ||
| Inverse Sum In-degree Index؛ vertex degree؛ Benzenoid Hydrocarbons | ||
| مراجع | ||
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[1] A. Ali, B. Furtula, and I. Gutman, Inverse sum indeg index: bounds and extremal results, Rocky M. J. Math. (2024).
[2] M. Arockiaraj, J.J.J. Godlin, and S. Radha, Comparative study of degree and neighborhood degree sum-based topological indices for predicting physicochemical properties of skin cancer drug structures, Mod. Phys. Lett. B 39 (2025), no. 25, 2550106. https://doi.org/10.1142/S0217984925501064
[3] M. Arockiaraj, D. Paul, J. Clement, S. Tigga, K. Jacob, and K. Balasubramanian, Novel molecular hybrid geometric-harmonic-Zagreb degree based descriptors and their efficacy in QSPR studies of polycyclic aromatic hydrocarbons, SAR QSAR Environ. Res. 34 (2023), no. 7, 569–589. https://doi.org/10.1080/1062936X.2023.2239149
[4] S. Balachandran, S. Elumalai, and T. Mansour, A short note on inverse sum indeg index of graphs, Asian-Eur. J. Math. 14 (2021), no. 1, 2050152. https://doi.org/10.1142/S1793557120501521
[5] B. Basavanagoud, M.H. Sunilkumar, and P.B. Anand, First neighbourhood Zagreb index of some nanostructures, Proc. Inst. Math. Mech. 7 (2018), no. 2, 178–193.
[6] K.C. Das and S. Mondal, On neighborhood inverse sum indeg index of molecular graphs with chemical significance, Inf. Sci. 623 (2023), 112–131. https://doi.org/10.1016/j.ins.2022.12.016
[7] A. Doley and A. Bharali, Some bounds on inverse sum indeg index of some graph operations, Adv. Appl. Discr. Math. 21 (2019), no. 2, 119–137. http://dx.doi.org/10.17654/DM021020119
[8] S. Elumalai, T. Mansour, and M.A. Rostami, New bounds on the hyper-Zagreb index for the simple connected graphs, Electron. J. Graph Theory Appl. 6 (2018), no. 1, 166–177.
[9] S. Fajtlowicz, On conjectures of graffiti-II, Congr. Numer 60 (1987), 187–97.
[10] F. Falahati-Nezhad, M. Azari, and T. Došlić, Sharp bounds on the inverse sum indeg index, Discrete Appl. Math. 217 (2017), no. 2, 185–195. https://doi.org/10.1016/j.dam.2016.09.014
[11] M. Ghorbani and M.A. Hosseinzadeh, A note of Zagreb indices of nanostar dendrimers, Optoelectron. Adv. Mat. 4 (2010), no. 11, 1877–1880.
[12] M. Ghorbani and M.A. Hosseinzadeh, The third version of Zagreb index, Discrete Math. Algorithms Appl. 5 (2013), no. 04, 1350039. https://doi.org/10.1142/S1793830913500390 [13] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total $\phi$-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535–538. https://doi.org/10.1016/0009-2614(72)85099-1
[14] P.J. Hansen and P.C. Jurs, Chemical applications of graph theory. part I. Fundamentals and topological indices, J. Chem. Educ. 65 (1988), no. 7, 574. https://doi.org/10.1021/ed065p574
[15] Ö.Ç. Havare, On the inverse sum indeg index of some graph operations, J. Egypt. Math. Soc. 28 (2020), no. 1, Article number: 28. https://doi.org/10.1186/s42787-020-00089-1
[16] F. Jamal and M. Imran, Bounds on sombor index and inverse sum indeg (ISI) index of graph operations, Commun. Comb. Optim. 9 (2024), no. 4, 785–798. https://doi.org/10.22049/cco.2023.28718.1684
[17] 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
[18] V.R. Kulli, General fifth m-Zagreb indices and fifth m-Zagreb polynomials of PAMAM dendrimers, Intern. J. Fuzzy Mathematical Archive 13 (2017), no. 1, 99–103. http://doi.org/10.22457/ijfma.v13n1a10
[19] V.R. Kulli, Degree based neighborhood indices of some nanostructures, SSRG Int. J. Appl. Chem. 7 (2020), no. 3, 63–68. https://doi.org/10.14445/23939133/IJAC-V7I3P105
[20] M.M. Matejić, I.Ź. Milovanović, and E.I. Milovanović, Upper bounds for the inverse sum indeg index of graphs, Discrete Appl. Math. 251 (2018), 258–267. https://doi.org/10.1016/j.dam.2018.05.060
[21] S. Mondal, M.A. Ali, N. De, and A. Pal, Bounds for neighborhood Zagreb index and its explicit expressions under some graph operations, Proyecciones (Antofagasta) 39 (2020), no. 4, 799–819. http://doi.org/10.22199/issn.0717-6279-2020-04-0050
[22] S. Mondal, N. De, and A. Pal, On neighborhood Zagreb index of product graphs, J. Mol. Struct. 1223 (2021), 129210. https://doi.org/10.1016/j.molstruc.2020.129210 [23] S. Nagarajan, P.M. Kumar, and K. Pattabiraman, Inverse sum indeg invariant of some graphs, Eur. J. Math. Appl. 1 (2021), 12.
[24] B.G. Pachpatte, Analytic Inequalities: Recent Advances, Springer Science & Business Media, 2012.
[25] K. Pattabiraman, Inverse sum indeg index of graphs, AKCE Int. J. Graphs Comb. 15 (2018), no. 2, 155–167. https://doi.org/10.1016/j.akcej.2017.06.001 [26] H.S. Ramane, K.S. Pise, R.B. Jummannaver, and D.D. Patil, On neighborhood Zagreb indices and coindices of graphs, Bulletin of the International Mathematical Virtual Institute 13 (2023), no. 1, 155–168. https://doi.org/10.7251/BIMVI2301155R
[27] H.S. Ramane, K.S. Pisea, R.B. Jummannaverb, and D.D. Patila, Applications of neighbors degree sum of a vertex on Zagreb indices, MATCH Commun. Math. Comput. Chem. 85 (2021), no. 2, 329–348.
[28] A. Rani, M. Imran, and U. Ali, Sharp bounds for the inverse sum indeg index of graph operations, Math. Probl. Eng. 2021 (2021), no. 1, 5561033. https://doi.org/10.1155/2021/5561033
[29] T. Réti, A. Ali, P. Varga, and E. Bitay, Some properties of the neighborhood first Zagreb index, Discrete Math. Lett. 2 (2019), 10–17.
[30] P. Sarkar, A. Pal, and S. Mondal, On some neighborhood degree-based structure descriptors and their applications to graphene, Eur. Phys. J. Plus 140 (2025), no. 1, 1–14. https://doi.org/10.1140/epjp/s13360-024-05939-w
[31] G.H. Shirdel, H. Rezapour, and A.M. Sayadi, The hyper-Zagreb index of graph operations, Iran. J. Math. Chem. 3 (2013), no. 2, 213–220.
[32] J.M. Sigarreta, Bounds for the geometric-arithmetic index of a graph, Miskolc Math. Notes 16 (2015), no. 2, 1199–1212. https://doi.org/10.18514/MMN.2015.1423[33] M.I. Stankevich, I.V. Stankevich, and N.S. Zefirov, Topological indices in organic chemistry, Russ. Chem. Rev. 57 (1988), no. 3, 191. https://doi.org/10.1070/RC1988v057n03ABEH003344
[34] D. Vukčević and M. Gašperov, Bond additive modeling 1. adriatic indices, Croat. Chem. Acta 83 (2010), no. 3, 243–260. | ||
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