آمار
| تعداد نشریات | 5 |
| تعداد شماره‌ها | 115 |
| تعداد مقالات | 1,304 |
| تعداد مشاهده مقاله | 1,290,358 |
| تعداد دریافت فایل اصل مقاله | 1,137,686 |
Neighborhood First Zagreb Index and Maximal Unicyclic and Bicyclic Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 شهریور 1403 اصل مقاله (585.69 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29450.2000 | ||
| نویسندگان | ||
| Waheed Khalid؛ Shamaila Yousaf* | ||
| Department of Mathematics , University of Gujrat, Hafiz Hayat Campus, Gujrat, Pakistan | ||
| چکیده | ||
| The Neighborhood First Zagreb Index $NM_{1}$ measures the topological properties of a molecular graph. Neighborhood First Zagreb Index $NM_{1}$ is defined as $NM_{1}(G) = \sum_{ v\in V (G)}(S(v))^{2}$, where $S(v)$ used to represent the sum of degrees of vertices adjacent to a vertex $v$ in a graph $G$. In this study, we focus on characterizing the graphs with the maximum neighborhood first Zagreb index in the class of unicyclic/bicyclic graphs on $n$ vertices, where $n$ is a fixed integer greater than or equal to $5$. Specifically, we are interested in identifying the graphs that have the highest value according to the recently introduced neighborhood first Zagreb index $NM_{1}$. | ||
| کلیدواژه‌ها | ||
| extremal graph theory؛ neighborhood topological index؛ different classes of graphs | ||
| مراجع | ||
|
[1] H. Abdo, D. Dimitrov, T. Réti, and D. Stevanović, Estimation of the spectral radius of graph by the second Zagreb index, MATCH Commun. Math. Comput. Chem. 72 (2014), no. 3, 741–751.
[2] A. Ali, I. Gutman, E. Milovanovćc, and I. Milovanović, Sum of powers of the degrees of graphs: extremal results and bounds, MATCH Commun. Math. Comput. Chem. 80 (2018), no. 1, 5–84.
[3] A. Ali, Z. Raza, and A.A. Bhatti, Bond incident degree (BID) indices of polyomino chains: a unified approach, Appl. Math. Comput. 287 (2016), 28–37. https://doi.org/10.1016/j.amc.2016.04.012 [4] A. Ali, L. Zhong, and I. Gutman, Harmonic index and its generalizations: extremal results and bounds, MATCH Commun. Math. Comput. Chem. 81 (2019), no. 2, 249–311.
[5] D. Bonchev and L.B. Kier, Topological atomic indices and the electronic charges in alkanes, J. Math. Chem. 9 (1992), no. 1, 75–85. https://doi.org/10.1007/BF01172931 [6] B. Borovićanin, K.C. Das, B. Furtula, and I. Gutman, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem. 78 (2017), 17–100.
[7] K.C. Das, Maximizing the sum of the squares of the degrees of a graph, Discrete Math. 285 (2004), no. 1-3, 57–66. https://doi.org/10.1016/j.disc.2004.04.007 [8] K.C. Das, K. Xu, and J. Nam, Zagreb indices of graphs, Front. Math. China 10 (2015), no. 3, 567–582. https://doi.org/10.1007/s11464-015-0431-9 [9] T. Došlić and T. Réti, Novel degree-based molecular descriptors with increased discriminating power, Acta Polytech. Hung. 9 (2012), no. 4, 17–30.
[10] S. Fajtlowicz, On conjectures of Graffiti-II, Congr. Numer 60 (1987), 187–97.
[11] M. Ghorbani and M.A. Hosseinzadeh, Computing ABC4 index of nanostar dendrimers, Optoelectron. Adv. Mat. 4 (2010), 1419–1422.
[12] C. Godsil and G. Royle, Algebraic Graph Theory, Springer New York, 2001.
[13] A. Graovac, M. Ghorbani, and M.A. Hosseinzadeh, Computing fifth geometric-arithmetic index for nanostar dendrimers, J. Disc. Math. Appl. 1 (2011), no. 1-2, 33–42. https://doi.org/10.22061/jmns.2011.461 [14] J.L. Gross and J. Yellen, Graph Theory, CRC Press, Boca Raton, Florida, 2000.
[15] I. Gutman, Degree-based topological indices, Croat. Chem. Acta, CCA) 86 (2013), no. 4, 351–361. http://dx.doi.org/10.5562/cca2294 [16] I. Gutman and K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004), 83–92.
[17] I. Gutman, E. Milovanović, and I. Milovanović, Beyond the Zagreb indices, AKCE Int. J. Graphs Comb. 17 (2020), no. 1, 74–85. https://doi.org/10.1016/j.akcej.2018.05.002 [18] I. Gutman and J. Tošović, Testing the quality of molecular structure descriptors. Vertex-degree-based topological indices, J. Serb. Chem. Soc. 78 (2013), no. 6, 805–810.
[19] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total ϕ-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535–538. https://doi.org/10.1016/0009-2614(72)85099-1 [20] I. Gutman, N. Trinajstić, and C.F. Wilcox, Graph theory and molecular orbitals. XII. Acyclic polyenes, J. Chem. Phys. 62 (1975), no. 9, 3399–3405. https://doi.org/10.1063/1.430994 [21] B. Liu and Z. You, A survey on comparing Zagreb indices, MATCH Commun. Math. Comput. Chem. 65 (2011), no. 3, 581–593.
[22] I.Z. Milovanovic, V.M. Ćirić, I. Milovanović, and E. Milovanović, On some spectral, vertex and edge degree–based graph invariants, MATCH Commun. Math. Comput. Chem 77 (2017), no. 1, 177–188.
[23] S. Mondal, N. De, and A. Pal, On neighborhood Zagreb index of product graphs, J. Mol. Struct. 1223 (2021), Article ID: 129210. https://doi.org/10.1016/j.molstruc.2020.129210 [24] S. Nikolić, G. Kovačević, A. Miličević, and N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), no. 2, 113–124.
[25] T. Réti, A. Ali, P. Varga, and E. Bitay, Some properties of the neighborhood first Zagreb index, Discrete Math. Lett. 2 (2019), 10–17.
[26] T. Réti, I. Gutman, and D. Vukičević, On Zagreb indices of pseudo-regular graphs, J. Discrete Math. Appl. 1 (2011), no. 1-2, 1–12. https://doi.org/10.22061/jmns.2011.458 [27] D. Stevanović, Spectral Radius of Graphs, Academic Press, Amsterdam, 2015.
[28] A.A. Toropov, A.P. Toropova, T.T. Ismailov, N.L. Voropaeva, and I.N. Ruban, Extended molecular connectivity: Prediction of boiling points of alkanes, J. Struct. Chem. 38 (1997), no. 6, 965–969. https://doi.org/10.1007/BF02763818 [29] S. Wang and B. Zhou, On the first extended zeroth-order connectivity index of trees, Iran. J. Sci. 38 (2014), no. 3, 213–219.
[30] S. Yousaf and A.A. Bhatti, On the minimal unicyclic and bicyclic graphs with respect to the neighborhood first Zagreb index, Iranian J. Math. Chem. 13 (2022), no. 2, 109–128. https://doi.org/10.22052/ijmc.2022.242939.1571 [31] A. Yu, M. Lu, and F. Tian, On the spectral radius of graphs, Linear Algebra Appl. 387 (2004), 41–49. https://doi.org/10.1016/j.laa.2004.01.020 [32] B. Zhou and N. Trinajstić, On extended connectivity indices, J. Math. Chem. 46 (2009), no. 4, 1172–1180. https://doi.org/10.1007/s10910-008-9500-6 | ||
|
آمار تعداد مشاهده مقاله: 175 تعداد دریافت فایل اصل مقاله: 280 |
||