University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 8 3 2017 09 01 Graphs with Smallest Forgotten Index 259 273 43258 10.22052/ijmc.2017.43258 EN I. Gutman University of Kragujevac, Serbia A. Ghalavand University of Kashan T. Dehghan-Zadeh University of Kashan A. R. Ashrafi University of Kashan Journal Article 2016 04 22 The forgotten topological index of a molecular graph G is defined as F(G)=\sum_{v\in V(G)}d^{3}(v), where d(u) denotes the degree of vertex u in G. The first through the sixth smallest forgotten indices among all trees, the first through the third smallest forgotten indices among all connected graph with cyclomatic number \gamma=1,2, the first through the fourth for \gamma=3, and the first and the second for \gamma=4,5 are determined. These results are compared with those obtained for the first Zagreb index. https://ijmc.kashanu.ac.ir/article_43258_60932aad8f9b423afed9a875153fe9a1.pdf