Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21282220170901On leap Zagreb indices of graphs991171364310.22049/cco.2017.25949.1059ENIvanGutmanUniversity of Kragujevac0000-0001-9681-1550Ahmed MNajiDepartment of Mathematics, University of Mysore, Mysusu, India0000-0003-0007-8927Nandappa DSonerDepartment of Mathematics, University of Mysore, Mysuru, IndiaJournal Article20170530The first and second Zagreb indices of a graph are equal, respectively, to the sum of squares of the vertex degrees, <br />and the sum of the products of the degrees of pairs of adjacent vertices. We now consider analogous graph invariants, based on the second degrees of vertices (number of their second neighbors), called leap Zagreb indices. A number of their basic properties is established.http://comb-opt.azaruniv.ac.ir/article_13643_fc88ed6fdf52b7f7a7ad4b621f695992.pdf