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A note on the first Zagreb index and coindex of graphs | ||
Communications in Combinatorics and Optimization | ||
مقاله 4، دوره 6، شماره 1، شهریور 2021، صفحه 41-51 اصل مقاله (375.42 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2020.26809.1144 | ||
نویسندگان | ||
Igor Milovanović* 1؛ Marjan Matejić2؛ Emina Milovanović2؛ Rana Khoeilar3 | ||
1Faculty of Electronic Engineering, Nis, Serbia | ||
2Faculty of Electronic Engineering | ||
3Azarbaijan Shahid Madani University | ||
چکیده | ||
Let $G=(V,E)$, $V=\{v_1,v_2,\ldots,v_n\}$, be a simple graph with $n$ vertices, $m$ edges and a sequence of vertex degrees $\Delta=d_1\ge d_2\ge \cdots \ge d_n=\delta$, $d_i=d(v_i)$. If vertices $v_i$ and $v_j$ are adjacent in $G$, it is denoted as $i\sim j$, otherwise, we write $i\nsim j$. The first Zagreb index is vertex-degree-based graph invariant defined as $M_1(G)=\sum_{i=1}^nd_i^2$, whereas the first Zagreb coindex is defined as $\overline{M}_1(G)=\sum_{i\nsim j} d_i+d_j)$. A couple of new upper and lower bounds for $M_1(G)$, as well as a new upper bound for $\overline{M}_1(G)$, are obtained. | ||
کلیدواژهها | ||
Topological indices؛ first Zagreb index؛ first Zagreb coindex | ||
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), no. 1, 5–84.
[2] A.R. Ashrafi, T. Došlić, and A. Hamzeh, The Zagreb coindices of graph operations, Discrete Appl. Math. 158 (2010), no. 15, 1571–1578.
[3] A.T. Balaban, I. Motoc, D. Bonchev, and O. Mekenyan, Topological indices for structure-activity correlations, Topics Curr. Chem. 114 (1983), 21–55.
[4] B. Borovicanin, K.C. Das, B. Furtula, and I. Gutman, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem. 78 (2017), no. 1, 17–100.
[5] , Zagreb indices: Bounds and extremal graphs, vol. In: I. Gutman, B. Furtula, K. C. Das, E. Milovanović, I. Milovanović (Eds.), Bounds in Chemical Graph Theory – Basics, Univ. Kragujevac, Kragujevac, 2017, pp. 67–153.
[6] V. Cirtoaje, The best lower bound depended on two fixed variables for Jensen’s inequality with ordered variables, J. Ineq. Appl. 2010 (2010), ID 12858.
[7] K. C. Das and I. Gutman, Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem. 52 (2004), no. 1, 103–112.
[8] K. C. Das, I. Gutman, and B. Horoldagva, New spectral indices for molecule description, MATCH Commun. Math. Comput. Chem. 68 (2012), no. 1, 189–198.
[9] K.C. Das, Maximizing the sum of the squares of the degrees of a graph, Discrete Math. 285 (2004), no. 1-3, 57–66.
[10] T. Došlić, Vertex–weighted Wiener polynomials for composite graphs, Ars Math. Contemp. 1 (2008), no. 1, 66–80.
[11] S. Fajtlowicz, On conjectures of Graffiti-II, Congr. Numer. 60 (1987), 187–197.
[12] I. Gutman and K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004), no. 1, 83–92.
[13] I. Gutman, I. Milovanović, and E. Milovanović, Relations between ordinary and multiplicative degree-based topological indices, Filomat 32 (2018), no. 8, 3031–3042.
[14] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total πelectron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535–538.
[15] J.L.W.V. Jensen, Sur les fonctions convexes et les inegalites entre les valeurs moyennes, Acta Math. 30 (1906), 175–193.
[16] D.S. Mitrinović, J.E. Pečarić, and A.M. Fink, Classical and New Inequalities in Analysis, Springer, Netherlands, 1993.
[17] S. Nikolić, G. Kovačević, A. Miličević, and N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), no. 2, 113–124.
[18] R. Rasi, S.M. Sheikholeslami, and A. Behmaram, An upper bound on the first Zagreb index in trees, Iranian J. Math. Chem. 8 (2017), no. 1, 71–82.
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