Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424118 | European Journal of Combinatorics | 2015 | 12 Pages |
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 (0â¤iâ¤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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Rui Yang, Heping Zhang,