Abstract
A(3,6)-fullerene is a connected cubic plane graph whose faces are only triangles and hexagons,and has the connectivity 2 or 3.The(3,6)-fullerenes with connectivity 2 are the tubes consisting of l concentric hexagonal layers such that each layer consists of two hexa-gons,capped on each end by two adjacent triangles,denoted by T1(l≥1).A(3,6)-fullerene T1 with n vertices has exactly 24+1 perfect matchings.The structure of a(3,6)-fullerene G with connectivity 3 can be determined by only three parameters r,s and t,thus we denote it by G=(r,s,t),where r is the radius(number of rings),s is the size(number of spokes in each layer,s ≥ 4,s is even),and t is the torsion(0≤t＜s,t≡r mod 2).In this paper,the counting formula of the perfect matchings in G=(n+1,4,t)is given,and the number of perfect match-ings is obtained.Therefore,the correctness of the conclusion that every bridgeless cubic graph with p vertices has at least 23656 perfect matchings proposed by Esperet et al is verified for(3,6)-fullerene G=(n+1,4,t).
基金项目
National Natural Science Foundation of China(11801148)
National Natural Science Foundation of China(11801149)
National Natural Science Foundation of China(11626089)
Foundation for the Doctor of Henan Polytechnic University(B2014-060)
NETL
NSTL
万方数据