Upper bound for the geometric-arithmetic index of trees with given domination number

Abstract

Given a graph G with vertex set V(G) and edge set E(G), the geometric-arithmetic index is the valueGA(G)=∑uv∈E(G)2dudvdu+dv, where du and dv denote the degrees of the vertices u,v∈V(G), respectively. In this work we present an upper bound for the geometric-arithmetic index of trees in terms of the order and the domination number, and we characterize the extremal trees for this upper bound. Finally, using a known relation between the geometric-arithmetic and arithmetic-geometric indices, we deduce a lower bound for the arithmetic-geometric index using the same parameters.