A connected graph is called of non-QE class if it does not admit a quadratic embedding in Euclidean space. primary contain as an isometrically embedded proper subgraph. The graphs on six vertices are completely classified into the classes QE graphs, and graphs.

the total irregularity of a graph g is defined as 〖irr〗_t (g)=1/2 ∑_(u,v∈v(g))▒〖|d_u-d_v |〗, where d_u denotes the degree of a vertex u∈v(g). in this paper by using the gini index, we obtain the ordering of the total irregularity index for some classes of connected graphs, with the same number of vertices.