On two types of geometric–arithmetic index

Recently a class of so-called ‘geometric–arithmetic’ topological indices ( GA ) was put forward, defined as the sum over all edges ( uv ) of a (molecular) graph G , of terms Q u Q v / 1 2 ( Q u + Q v ) , where Q u is some quantity associated with the vertex u of G . One variant of GA was obtained for Q u is the number of vertices of G , lying closer to vertex u than to vertex v . We obtain bounds for this GA -index, and also put forward an analogous one, for which Q u is the number of edges of G , lying closer to vertex u than to vertex v .