2-resonant fullerenes. (October 2015) - Yang, Rui; Zhang, Heping
Abstract: A fullerene graph F is a planar cubic graph with exactly 12 pentagonal faces and other hexagonal faces. A set H of disjoint hexagons of F is called a resonant pattern (or sextet pattern ) if F has a perfect matching M such that every hexagon in H is M -alternating. F is said to be k - resonant if any i ( 0 ≤ i ≤ k ) disjoint hexagons of F form a resonant pattern. It was known that each fullerene graph is 1-resonant and there are only nine fullerene graphs that are 3-resonant. In this paper, we show that the fullerene graphs which do not contain the subgraph L or R as illustrated in Fig. 1 are 2-resonant except for the specific eleven graphs. This result implies that each IPR fullerene is 2-resonant.