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 ...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 hexangons,capped on each end by two adjacent triangles,denoted by T_(l)(l≥1).A(3,6)-fullerene Tl with n vertices has exactly 2n/4+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 matchpings is obtained.Therefore,the correctness of the conclusion that every bridgeless cubic graph with p vertices has at least 2p/3656perfect matchings proposed by Esperet et al is verified for(3,6)-fullerene G=(n+1,4,t).展开更多
基金Supported by National Natural Science Foundation of China(11801148,11801149 and 11626089)the Foundation for the Doctor of Henan Polytechnic University(B2014-060)
文摘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 hexangons,capped on each end by two adjacent triangles,denoted by T_(l)(l≥1).A(3,6)-fullerene Tl with n vertices has exactly 2n/4+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 matchpings is obtained.Therefore,the correctness of the conclusion that every bridgeless cubic graph with p vertices has at least 2p/3656perfect matchings proposed by Esperet et al is verified for(3,6)-fullerene G=(n+1,4,t).
