Some new bounds on the general sum--connectivity index

Ali, Akbar; Javaid, Mubeen; Matejić, Marjan; Milovanović, Igor; Milovanović, Emina

doi:10.22049/cco.2019.26618.1125

تعداد نشریات	5
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	Some new bounds on the general sum--connectivity index
Communications in Combinatorics and Optimization
مقاله 2، دوره 5، شماره 2، اسفند 2020، صفحه 97-109 اصل مقاله (390.27 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2019.26618.1125
نویسندگان
Akbar Ali¹؛ Mubeen Javaid¹؛ Marjan Matejić²؛ Igor Milovanović^* ³؛ Emina Milovanović²
¹Knowledge Unit of Science University of Management and Technology, Sialkot 51310, Pakistan
²Faculty of Electronic Engineering, 18000 Nis, Serbia
³Faculty of Electronic Engineering, Nis, Serbia
چکیده
Let $G=(V,E)$ be a simple connected graph with $n$ vertices, $m$ edges and sequence of vertex degrees $d_1 \ge d_2 \ge \cdots \ge d_n>0$, $d_i=d(v_i)$, where $v_i\in V$. With $i\sim j$ we denote adjacency of vertices $v_i$ and $v_j$. The general sum--connectivity index of graph is defined as $\chi_{\alpha}(G)=\sum_{i\sim j}(d_i+d_j)^{\alpha}$, where $\alpha$ is an arbitrary real number. In this paper we determine relations between $\chi_{\alpha+\beta}(G)$ and $\chi_{\alpha+\beta-1}(G)$, where $\alpha$ and $\beta$ are arbitrary real numbers, and obtain new bounds for $\chi_{\alpha}(G)$. Also, by the appropriate choice of parameters $\alpha$ and $\beta$, we obtain a number of old/new inequalities for different vertex--degree--based topological indices.
کلیدواژه‌ها
Topological indices؛ vertex degree؛ sum-connectivity index

مراجع
[1] A. Ali, I. Gutman, E. Milovanović, and I. Milovanović, Sum of powers of the degrees of graphs: extremal results and bounds, MATCH Commun. Math. Comput. Chem. 80 (2018), 5–84. [2] A. Ali, L. Zhong, and I. Gutman, Harmonic index and its generalizations: extremal results and bounds, MATCH Commun. Math. Comput. Chem. 81 (2019), 249–311. [3] B. Borovićanin, K.C. Das, B. Furtula, and I. Gutman, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem 78 (2017), no. 1, 17–100. [4] K.C. Das, S. Das, and B. Zhou, Sum-connectivity index of a graph, Front. Math. China 11 (2016), no. 1, 47–54. [5] T. Došlic, B. Furtula, A. Graovac, I. Gutman, S. Moradi, and Z. Yarahmadi, On vertex-degree-based molecular structure descriptors, MATCH Commun. Math. Comput. Chem. 66 (2011), no. 2, 613–626. [6] C. Elphick and P. Wocjan, Bounds and power means for the general Randić and sum-connectivity indices, In: Bounds in Chemical Graph Theory – Mainstreams, I. Gutman, B. Furtula, K.C. Das, E.Milovanović, I.Milovanović, Eds.), Mathematical Chemistry Monographs - MCM 19, Univ. Kragujevac, Kragujevac, 2017, pp. 121–133. [7] S. Fajtlowicz, On conjectures of graffiti-II, Congr. Numer. 60 (1987), 187–197. [8] F. Falahati-Nezhad and M. Azari, Bounds on the hyper-Zagreb index, J. Appl. Math. Inform. 34 (2016), no. 3-4, 319–330. [9] B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015), no. 4, 1184–1190. [10] I. Gutman and K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004), no. 1, 83–92. [11] I. Gutman, E. Milovanović, and I. Milovanović, Beyond the Zagreb indices, AKCE Int. J. Graph Combin. (to appear). [12] I. Gutman, B. Ruščić, N. Trinajstić, and C.F. Wilcox, Graph theory and molecular orbitals. XII. acyclic polyenes, J. Chem. Phys. 62 (1975), no. 9, 3399–3405. [13] 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. [14] M. Matejić, E. Milovanović, and I. Milovanović, On bounds for harmonic topological index, Filomat 32 (2018), no. 1, 311–317. [15] M. Matejić, E. Milovanović, and I. Milovanović, On lower bounds for VDB topological indices of graphs, Appl. Math. Comput. Sci. 3 (2018), no. 1, 5–11. [16] M. Matejić, E. Milovanović, and I. Milovanović, Some inequalities for general sum–connectivity index, MATCH Commun. Math. Comput. Chem. 79 (2018), 477–489. [17] E. Milovanović, I. Milovanović, I. Gutman, and B. Furtula, Some inequalities for general sum–connectivity index, Int. J. Appl. Graph Theory 1, no. 1. 1--15 [18] D.S. Mitrinović, J.E. Pečarić, and A.M. Fink, Classical and new inequalities in analysis, Kluwer Academic Publishers, Dordrecht, 1993. [19] D.S. Mitrinović and P.M. Vasić, Analytic inequalities, Springer Verlag, BerlinHeidelberg-New York, 1970. [20] S. Nikolić, G. Kovačević, A. Miličević, and N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), no. 2, 113–124. [21] J. Radon, Über die absolut additiven mengenfunktionen, Wiener Sitzungsber 122 (1913), 1295–1438. [22] T. Réti and I. Felde, Novel Zagreb indices-based inequalities with particular regard to semiregular and generalized semiregular graphs, MATCH Commun. Math. Comput. Chem. 76 (2016), 185–206. [23] J.M. Rodríguez, J.L. Sánchez, and J.M. Sigarreta, CMMSE-on the first general Zagreb index, J. Math. Chem. 56 (2018), no. 7, 1849–1864. [24] J.M. Rodríguez and J.M. Sigarreta, The harmonic index, In: Bounds in Chemical Graph Theory – Basics, (I. Gutman, B. Furtula, K. C. Das, E. Milovanović, I. Milovanović, Eds.), Mathematical Chemistry Monographs - MCM 19, Univ. Kragujevac, Kragujevac, 2017, pp. 229–281. [25] J.M. Rodríguez and J.M. Sigarreta, New results on the harmonic index and its generalizations, MATCH Commun. Math. Comput. Chem. 78 (2017), 387–404. [26] G.H. Shirdel, H. Rezapour, and A.M. Sayadi, The hyper-Zagreb index of graph operations, Iranian J. Math. Chem. 4 (2013), no. 2, 213–220. [27] L. Zhong and K. Xu, Inequalities between vertex-degree-based topological indices, MATCH Commun. Math. Comput. Chem. 71 (2014), no. 3, 627–642. [28] B. Zhou and N. Trinajstić, On a novel connectivity index, J. Math. Chem. 46 (2009), no. 4, 1252–1270. [29] B. Zhou and N. Trinajstić, On general sum-connectivity index, J. Math. Chem. 47 (2010), no. 1, 210–218. [30] B. Zhou and N. Trinajstić, Relations between the product-and sum-connectivity indices, Croat. Chem. Acta 85 (2012), no. 3, 363–365.
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Some new bounds on the general sum--connectivity index