eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2016-01-15 4 1 8 15 10.12691/tjant-4-1-2 TJANT2016412 article T. Mansour 1 M. A. Rostami 2 E. Suresh sureshkako@gmail.com 3 G. B. A. Xavier 4 Department of Mathematics, University of Haifa, 3498838 Haifa, Israel Institute for Computer Science, Friedrich Schiller University Jena, Germany Department of Mathematics, Velammal Engineering College, Surapet, Chennai-66, Tamil Nadu, India Department of Mathematics, Sacred Heart College, Tirupattur-635601, Tamil Nadu, India The edge version of traditional first Zagreb index is known as first reformulated Zagreb index. In this paper, we analyze and compare various lower and upper bounds for the first reformulated Zagreb index and we propose new lower and upper bounds which are stronger than the existing and recent results [Appl. Math. Comp. 273 (2016) 16-20]. In addition, we prove that our bounds are superior in comparison with the other existing bounds. http://pubs.sciepub.com/tjant/4/1/2/tjant-4-1-2.pdf Zagreb indices first reformulated Zagreb index forgotten topological index