a note on polyomino chains with extremum general sum-connectivity index

The general sum-connectivity index of a graph g is defined as χα(g)=∑uv∈e(g)(du+dv)^α where du is degree of the vertex u∈v(g), α is a real number different from 0 and uv is the edge connecting the vertices u,v. in this note, the problem of characterizing the graphs having extremum χα values from a certain collection of polyomino chain graphs is solved for α<0. the obtained results together with already known results (concerning extremum χα values of polyomino chain graphs) give the complete solution of the aforementioned problem.