General degree distance of graphs

We generalize several topological indices and introduce the general degree distance of a connected graph $G$. For $a, b \in \mathbb{R}$, $DD_{a,b} (G) = \sum_{ v V(G)} [deg_{G}(v)]^a S^b_{G} (v)$, where $V(G)$ is vertex set $G$, $deg_G (v)$ $v$, $S^b_{G} (v) w V(G) \setminus \{ \} } [d_{G} (v,w) ]^{b}$ $d_{G} (v,w)$ between $v$ $w$ in present some sharp bounds on for multipartite graphs trees given order, order chromatic number, connectivity, number pendant vertices.