ESTIMATING THE SECOND AND THIRD GEOMETRIC-ARITHMETIC INDICES

Arithmetic–geometric indices are graph invariants defined as the sum of terms √Qu Qv/[(Qu +Qv)/2] over all edges uv of the graph, where Qu is some quantity associated with the vertex u. If Qu is the number of vertices (resp. edges) lying closer to u than to v, then one speaks of the second (resp. third) geometric–arithmetic index, GA2 and GA3. We obtain inequalities between GA2 and GA3 for trees, revealing that the main parameters determining their relation are the number of vertices and the number of pendent vertices.