study of fullerenes by symmetry-based invariants

چکیده مقاله

A molecular graph is a graph with vertices as atoms of a molecule M and edges are chemical bonds of M. A graph is called tri-connected, if there does not exist two vertices whose removal disconnects the graph. A (k,6)-fullerene graph is a cubic, planar and tri-connected graph whose faces are all k-gons or hexagons. By Euler theorem, it can be proved that k=3, 4 or 5. A fullerene is a molecule that its molecular graph is a (k,6)-fullerene graph, for some k. Graovac and Pisanski in 1991 proposed an algebraic modufication of the well-known Wiener index of a graph by considering its automorphism group. In this talk, we report our result for some classes of fullerenes.