Page | 827 Received: 28 March 2020 Revised: 17 May 2020 Accepted: 18 May 2020 DOI: 10.33945/SAMI/ECC.2020.7.10 Eurasian Chem. Commun. 2 (2020) 827-833 http:/echemcom.com FULL PAPER F-leap index of some special classes of bridge and chain graphs Mohanad Ali Mohammed a |Raad Sehen Haoer a |Janet Robert b |Natarajan Chidambaram b, * |Narasimhan Devadoss b a Department of Mathematics, Open Educational College, Ministry of Education, Al Qadisiya Centre, Iraq b Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed University, Kumbakonam, Tamil Nadu, India *Corresponding Author: Natarajan Chidambaram Tel.:+91-9952529575 The 2-degree of a vertex v in a (molecular) graph G is the number of vertices which are at distance two from v in G. The F-leap index of a molecular graph G is the sum of cubes of the 2-degree of every vertex v in G. In this research study, we have computed the F-leap index of some special classes of bridges and chain graphs. We also have determined the F-leap index of some chemical structures including polyphenyl chains and spiro chains. KEYWORDS Leap Zagreb indices; F-leap index; bridge; polyphenyl chain; spiro chain. Introduction A Topological index also known as connectivity index is a type of molecular descriptor that is calculated based on the molecular graph of a chemical compound. It is a numerical parameter of a graph which characterizes its topology and usually graphs invariant. According to [2] topological indices are extensively used as molecular descriptors in building:  QSAR-Quantitative Structure-Activity Relationship which are extensively used in pharmaceutical and agricultural chemistry for screening compound.  QSPR-Quantitative Structure-Property Relationship.  QSTR-Quantitative Structure-Toxicity Relations which is used in predicting toxicity of chemicals. These have become a powerful tools in contemporary chemical and medicinal research as it is possible to predict the biological activity, specific chemical activity, toxicity and the environmental fate even before its synthesis. An important and oldest topological index introduced by Gutman and Trinajstić [5], and Zagreb index study of structure property and correlation of molecules. They are namely first and second Zagreb indices and defined as follows:        ) ( ) ( 2 1 )] deg( ) [deg( ) deg( ) ( G E uv G V u v u u G M  2 ( ) 1 ( ) deg( ) deg( ) uv E G M G u v    Furtula and Gutman [4] defined F-index of graph G as:  3 ( ) 2 2 ( ) ( ) deg( ) [deg( ) deg( ) ] 2 uVG uv E G FG u u v        Azari et al. [1] found some interesting results on Zagreb indices of bridges and chain graphs. Infact this is the first seminal paper on topological indices of bridges and chain graph structures .In [8], Nilanjan De computed exact values for the F-index of bridge and chain graphs. Naji et al. [7] introduced graph invariants based on 2-degree of vertices called Leap Zagreb indices. The 2-degree of a vertex v in G is defined as the number of vertices which are