A generalized version of symmetric division degree index

Abstract

The symmetric division degree $SDD$-index of a simple connected graph $G$ is defined as the sum of terms $f(d_u,d_v)=(d_u/d_v)+(d_v/d_u)$ over all pairs of distinct adjacent vertices of $G$; where $d_u$ 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 $f(d_u,d_v)$ 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.