M. Saki - Department of Mathematics, Sousangerd Branch, Islamic Azad University, Sousangerd, Iran

we consider the second of the edge version of geometric – arithmetic index of graphs belonging to the class of geometric- arithmetic indices. Its related to the new versions of vertex Szeged index and PI index of line graphs. The main properties of are considered, such as upper and lower bounds. We compare the second version of the edge geometric–arithmetic indices for some graphs, TUC۴C۶C۸ [p,q]nanotorus and molecular octane isomers.

Geometric – arithmetic index, Line graph, Octane isomers, Molecular graph, Nanotorus