en تخصصي Special ECWMC 2018 <div style="text-align: justify;">Topological indices are widely used as mathematical tools to analyze different types of graphs emerged in a broad range of applications. The Hyper-Zagreb index (HM) is an important tool because it integrates the first two Zagreb indices. In this paper, we characterize the trees and unicyclic graphs with the first four and first eight greatest HM-value, respectively.</div> Hyper-Zagreb index, Vertex degree, Unicyclic graphs, Trees. 41 54 http://ijmsi.ir/browse.php?a_code=A-10-3673-1&slc_lang=en&sid=1 Hassan Rezapour hassan.rezapour@gmail.com 100319475328460010008 100319475328460010008 No Department of Mathematics, Faculty of Basic Sciences, University of Qom, Qom, Iran Ramin Nasiri R.Nasiri@Shahabdanesh.ac.ir 100319475328460010009 100319475328460010009 Yes Department of Mathematics, Faculty of Sciences, Imam Hossein Comprehensive University, Tehran, Iran Seyedahmad Mousavi smousav1@umbc.edu 100319475328460010010 100319475328460010010 No Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD 21250, U.S.A.