Extremal polyomino chains of VDB topological indices

Abstract

ABSTRACT: We show that the zig-zag chain Z 3 n of segments of length 3 (see Figure 2) has the minimal ABC index among all polyomino chains with n squares. More generally, we give conditions on the numbers {ϕij} under which the zig-zag chain Z 3 n is an extremal value of the induced topological index T defined by T (G) = X 1≤i≤j≤n−1 mijϕij where G is a graph with n vertices and mij is the number of edges of G with terminal vertices of degree i and j. We also find extremal values of the general Randi´c index Rα over the set of all polyomino chains, for some values of α.