Unicyclic Graphs With Minimum GA Index And Bicyclic Graphs With Minimum GA₂ Index

The geometric-arithmetic index was conceived by Vukicevic in 2009,defined as GA(G)=?(?),and it based on the end-vertex degree of all edges of a graph,in mathematical chemistry.The predictive power of the geometric-arithmetic index for physico-chemical properties is somewhat better that the one of Randic connectivity index.In 2011,Du et al.determined the first six maximum values for the GA indices of unicyclic graphs.The second geometric-arithmetic index GA₂ was conceived by Fath-Tabaret al.in 2010,and defined as GA₂(G)=?(?).They gave the lower and upper bounds for the GA₂ index,identified the trees with the minimum and the maximum GA₂ indices,which are the star and the path.In this paper,we will present a further ordering for the molecular unicyclic graphs,which exchange the number of the pendant paths,determine the seventh to eleventh maximum GA indices,and we determine the two kinds of bicyclic graphs with minimum GA₂.