Topological Indices and Their Applications to Circumcised Donut Benzenoid Systems, Kekulenes and Drugs

ABSTRACT

This paper describes a new technique to compute topological indices of donut benzenoids and Kekulenes with applications to drugs by dissecting the original topological network into smaller strength-weighted quotient graphs relative to the transitive closure of the Djokovi$\acute{c}$–Winkler relation. We have applied this technique to a series of donut benzenoid graphs obtained by circumcising at least two internal hexagons from parent benzenoid graphs. Such donut coronoid graph finds significant applications in emerging chemical materials of importance to synthetic organic chemistry and drug industry. It comprised of donut coronoid structures such as Kekulenes and related circumscribed structures where a number of graph-theoretical based techniques, such as resonance theory and Clar’s sextets. In this work, we have computed a number of topological indices of these donut coronoid systems such as the Wiener index, variants of Szeged, Schultz and Gutman indices.

KEYWORDS:

• Convex subgraph topologies
• coronoid systems
• Kekulenes
• QSAR and SAR relevant to drugs
• topological indices