I have been reading graph theory related to topological indices. I also found a question which is related to topological index (G.A. index) and clique number.
Let $G$ be a graph and $\omega$ be the clique number of the graph. The G.A index [$(\sum_{I,j \in E(G)} \frac{2\sqrt {d_i d_j}}{d_i+d_j})$ where, $d_i$ and $d_j$ are the vertex degree]. then,
$G.A. \ge \frac {\omega (\omega -1)}{2}$.
Here the equality holds if and only iff G is the complete graph.
Any help would be appreciated.