On some vertex-degree-based topological indices of hexagonal chemical graphs

The degree of a vertex of a (molecular) graph is the number of neighbor vertices of the vertex. A large number of molecu- lar graph based structure descriptors (topological indices) that depend on vertex degrees have been conceived. Topological indices, as numerical functions of (usually hydrogen-suppressed) molecular graph, represent an important type of molecular descriptors. These are important in QSAR and QSPR studies to relate biological or chemical properties of molecules to specific molecular descriptors, thus enabling prediction of properties of molecules based on their structure only and without their synthetization. In this paper we present our results on computation of various topological indices for chemical graphs with hexagonal or honey- comb structure. In particular, the Randić index, generalized Randić index, geometric-arithmetic index, Zagreb index, and some others, are studied. We also propose a topological classification of fullerenes based on double bonds in pentagons of the fullerenes. Then, graph isomorphism algorithms using topological indices, e.g. Wiener and Randić indices, of hexagonal chemical graphs are discussed and comparative analysis based on computations is presented. Some directions of future research are briefly outlined.