Extremal values of vertex-degree-based topological indices of coronoid systems

A vertex-degree-based (VDB for short) topological index phi induced by the numbers {phi(i,j)}, is defined for a graph G with n vertices as phi(G) = Sigma(1 <= i <= j <= n-1) m(i,j)phi(i,j), where m(i,j) is the number of edges in G joining vertices of degree i and j. Our main concern is to study VDB topological indices over important classes of coronoid systems. Recall that a coronoid system is a natural representation of a coronoid hydrocarbon and can be defined as a benzenoid-like system with a hole. In this paper we determine the extremal values of a VDB topological index phi over the set of primitive coronoid systems, the set of catacondensed coronoid systems, and the set of circumscribed coronoid systems.