A generalized version of symmetric division degree index

The symmetric division degree sdd-index of a simple connected graph g is defined as the sum of terms f (du,dv) = (du/dv) + (dv/du) over all pairs of distinct adjacent vertices of g; where du denotes the degree of a vertex u of graph g. in this paper, we introduce the general form of symmetric division degree index by replacing the degree of vertices f (du,dv) with another symmetric function of vertex properties. we establish some properties of the generalized symmetric division degree index gsdd index for certain special functions and calculate the values of these new indices for some well-known graphs.