A large number of topological indices of the form ∑ uv∈E(G) F(du, dv) are studied in mathematical chemistry, where uv denotes the edge of the graph G connecting the vertices u and v, and du is the degree of the vertex u. Among them the variable inverse sum deg index ISDa, with F(du, dv) = 1/(dau+dav). The aim of this paper is to obtain new mathematical properties for the ISD index and to characterize extremal graphs with respect to them. In the same sense, a quantitative structure property relationship (QSPR) study of this index was performed.