Results 1 
5 of
5
Extremal fullerene graphs with the maximum Clar number
, 801
"... A fullerene graph is a cubic 3connected plane graph with (exactly 12) pentagonal faces and hexagonal faces. Let Fn be a fullerene graph with n vertices. A set H of mutually disjoint hexagons of Fn is a sextet pattern if Fn has a perfect matching which alternates on and off each hexagon in H. The ma ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
A fullerene graph is a cubic 3connected plane graph with (exactly 12) pentagonal faces and hexagonal faces. Let Fn be a fullerene graph with n vertices. A set H of mutually disjoint hexagons of Fn is a sextet pattern if Fn has a perfect matching which alternates on and off each hexagon in H. The maximum cardinality of sextet patterns of Fn is the Clar number of Fn. It was shown that the Clar number is no more than ⌊n−12 6 ⌋. Many fullerenes with experimental evidence attain the upper bound, for instance, C60 and C70. In this paper, we characterize extremal fullerene graphs whose Clar numbers equal n−12 6. By the characterization, we show that there are precisely 18 fullerene graphs with 60 vertices, including C60, achieving the maximum Clar number 8 and we construct all these extremal fullerene graphs.
On kresonant fullerene graphs ∗
, 801
"... A fullerene graph F is a 3connected plane cubic graph with exactly 12 pentagons and the remaining hexagons. Let M be a perfect matching of F. A cycle C of F is Malternating if the edges of C appear alternately in and off M. A set H of disjoint hexagons of F is called a resonant pattern (or sextet ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
A fullerene graph F is a 3connected plane cubic graph with exactly 12 pentagons and the remaining hexagons. Let M be a perfect matching of F. A cycle C of F is Malternating if the edges of C appear alternately in and off M. 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 all hexagons in H are Malternating. A fullerene graph F is kresonant if any i (0 ≤ i ≤ k) disjoint hexagons of F form a resonant pattern. In this paper, we prove that every hexagon of a fullerene graph is resonant and all leapfrog fullerene graphs are 2resonant. Further, we show that a 3resonant fullerene graph has at most 60 vertices and construct all nine 3resonant fullerene graphs, which are also kresonant for every integer k> 3. Finally, sextet polynomials of the 3resonant fullerene graphs are computed.
CYCLIC 7EDGECUTS IN FULLERENE GRAPHS
"... A fullerene graph is a planar cubic graph whose all faces are pentagonal and hexagonal. The structure of cyclic edgecuts of fullerene graphs of sizes at most 6 is known. In the paper we study cyclic 7edge connectivity of fullerene graphs, distinguishing between degenerated and nondegenerated cycl ..."
Abstract
 Add to MetaCart
A fullerene graph is a planar cubic graph whose all faces are pentagonal and hexagonal. The structure of cyclic edgecuts of fullerene graphs of sizes at most 6 is known. In the paper we study cyclic 7edge connectivity of fullerene graphs, distinguishing between degenerated and nondegenerated cyclic edgecuts, regarding the arrangement of the 12 pentagons. We prove that if there exists a nondegenerated cyclic 7edgecut in a fullerene graph, then the graph is a nanotube unless it is one of the two exceptions presented. We determined that there are 57 configurations of degenerated cyclic 7edgecuts, and we listed all of them.
On the 2resonance of fullerenes ∗
, 2010
"... 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]. 1 ..."
Abstract
 Add to MetaCart
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]. 1