New results on symmetric division deg index

The symmetric division deg index (or simplysdd-index) was proposed by Vukicevic et al. as a remarkable predictor of total surface area of polychlorobiphenyls. It is one of discrete Adriatic indices that showed good predictive properties on the testing sets provided by International Academy of Mathematical Chemistry. In this paper, we investigate some properties of this graph invariant in terms of orbit structure of a graph and then we explore new bounds forsdd-index. In continuing, the inverse symmetric division deg index is defined and new results concerning these two graph indices are stablished. Finally, some bounds for both indices are presented.