Molecular Graphs with Extremal First Geometric-arithmetic Index

Abstract

Let $MG(i,n)$ be a connected molecular graph without multiple edges on $n$vertices whose minimum degree of vertices is $i$, where $i\le i\le 4$. One of the newest topological indices is the first Geometric-Arithmetic index. In this paper, we determine the graph with the minimum and the maximum value of the first Geometric-Arithmetic index in the family of graphs $MG(i,n)$,$l\le i\le 3$.