2 research outputs found
2-Resonant fullerenes
A fullerene graph is a planar cubic graph with exactly 12 pentagonal
faces and other hexagonal faces. A set of disjoint hexagons of
is called a resonant pattern (or sextet pattern) if has a perfect
matching such that every hexagon in is -alternating.
is said to be -resonant if any () disjoint hexagons of
form a resonant pattern. It was known that each fullerene graph is
1-resonant and all 3-resonant fullerenes are only the nine graphs. In this
paper, we show that the fullerene graphs which do not contain the subgraph
or as illustrated in Fig. 1 are 2-resonant except for the specific eleven
graphs. This result implies that each IPR fullerene is 2-resonant.Comment: 34 pages, 25 figure
On the 2-resonance of fullerenes
We show that every pair of hexagons in a fullerene graph satisfying the isolated pentagon rule (IPR) forms a resonant pattern. This solves a problem raised by Ye et al. [SIAM J. Discrete Math. 23(2):2009, p. 1023–1044]