By swapping out atoms for vertices and bonds edges, a graph may be used to model any molecular structure. A G is considered chemical in theory if no vertex of has degree 5 or greater. The bond incident (BID) index defined as the total contributions f(dG(u),dG(v)) from all edges uv G, where dG(w) stands w E(G) set f real-valued symmetric function. This paper addresses problem finding graphs with...