Graph theoretical invariants and elementary subgraphs of polyhex and polypent/polyhex systems of chemical relevance

Starting with the major graph theoretical invariants of n = No. of vertices (points), q = No. of edges (lines), and r = No. of rings (independent circuits) and Euler's fundamental equation of (r + 1) - q + n = 2, a myriad of invariants have evolved for describing the properties of molecular graphs (graphs representing molecules). The concepts of the aufbau principle, a periodic table set, the excised internal structure (a type of subgraph), the circumscribing operation, and the leapfrog operation have led to the development of algorithms that are highly useful for understanding and studying the structural properties of the classes of molecules that are isomorphic to the polyhex and polypent/polyhex graphs. These concepts will be reviewed and illustrated.