Remarks on first Zagreb indices
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 1, pp. 71-75 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $G$ be an undirected connected graph with $n\ge2$ vertices and $m$ edges. In this paper we are concerned with inequalities that reveal connections between graph invariants called first Zagreb index and reformulated first Zagreb index. Some of the obtained results represent generalization of the known inequalities.
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I. Ž. Milovanović; E. I. Milovanović. Remarks on first Zagreb indices. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 1, pp. 71-75. http://geodesic.mathdoc.fr/item/VMJ_2016_18_1_a8/

[1] Andrica D., Badea C., “Grüs inequality for positive linear functionals”, Period. Math. Hungar., 19:2 (1988), 155–167 | DOI | MR | Zbl

[2] Balaban A. T., Motoc I., Bonchev D., Mekenyan D., “Topological indices for structure activity correlations”, Topics Curr. Chem., 114 (1983), 21–55 | DOI

[3] Bhatia R., Davis C., “A better bound on the variance”, Amer. Math. Monthly, 107 (2000), 353–357 | DOI | MR | Zbl

[4] Caen D., “An upper bound on the sum of squares of degrees in a graph”, Discrete Math., 185:1–3 (1998), 245–248 | DOI | MR | Zbl

[5] De N., “Some bounds of reformulated Zagreb indices”, Appl. Math. Sci., 6:101 (2012), 505–512 | MR

[6] De N., “Reformulated Zagreb indices of dendrimers”, Math. Aeterna, 3:2 (2013), 133–138 | MR | Zbl

[7] Edwards C. S., “The largest vertex degree sum for a triangle in a graph”, Bul. London Math. Soc., 9 (1977), 203–208 | DOI | MR | Zbl

[8] Gutman I., Trinajstić N., “Graph theory and molecular orbitas. Total $\pi$-electron energy of alternant hydrocarbons”, Chem. Phys. Letters, 17 (1972), 535–538 | DOI

[9] Milićević A., Nikolić S., Trinajstić N., “On reformulated Zagreb indices”, Mol. Divers., 8:4 (2004), 393–399 | DOI

[10] Nagy J. V. S., “Über algebraische Gleichungen mit lauter reellen Wurzeln”, Jahresbericht der deutschen mathematiker-Vereingung, 27 (1918), 37–43 | Zbl

[11] Sharma R., Gupta M., Kapoor G., “Some better bounds on the variance with applications”, J. Math. Ineq., 4:3 (2010), 355–363 | DOI | MR | Zbl

[12] Todeschini R., Consonni V., Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, 2000