University of KashanIranian Journal of Mathematical Chemistry2228-648910420191201Some Results on Forgotten Topological Coindex30731810251210.22052/ijmc.2019.174722.1432ENMahdieh AzariKazerun Branch, Islamic Azad University0000-0002-0919-0598Farzaneh Falahati-NezhedSafadasht Branch, Islamic Azad UniversityJournal Article20190310The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph <em>G</em> as the sum of the terms <em>d<sub>u</sub></em><sup>2</sup>+<em>d<sub>v</sub></em><sup>2</sup> over all non-adjacent vertex pairs <em>uv</em> of <em>G</em>, where <em>d<sub>u</sub></em> denotes the degree of the vertex <em>u</em> in <em>G</em>. In this paper, we present some inequalities for the forgotten topological coindex in terms of some graph parameters such as the order, size, number of pendent vertices, minimal and maximal vertex degrees, and minimal non-pendent vertex degree. We also study the relation between this invariant and some well-known graph invariants such as the Zagreb indices and coindices, multiplicative Zagreb indices and coindices, Zagreb eccentricity indices, eccentric connectivity index and coindex, and total eccentricity. Exact formulae for computing the forgotten topological coindex of double graphs and extended double cover of a given graph are also proposed.https://ijmc.kashanu.ac.ir/article_102512_f335e16389378c0cec788b4cc1719e46.pdf