Abstract A vertex‐degree‐based (VDB for short) topological index φ induced by the numbers { φ i , j } , is defined for a graph G with n vertices as urn:x-wiley:00207608:media:qua26536:qua26536-math-0001 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 φ over the set of primitive coronoid systems, the set of catacondensed coronoid systems, and the set of circumscribed coronoid systems.