If G is a (molecular) graph with n vertices, and di is the degree of its i-th vertex, then the sum-connectivity index of G is the sum of the weights (du + dv)-1/2 of all edges uv of G. A polyomino system is a finite 2-connected plane graph such that each interior face (or say a cell) is surrounded by a regular square of length one. Formulas for calculating the sum-co...