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
The conception of orthomorphism has been generalized in this paper, and a counting formula on the generalized linear orthomorphism in the vector space over the Galois field with the arbitrary prime number p as the cha...The conception of orthomorphism has been generalized in this paper, and a counting formula on the generalized linear orthomorphism in the vector space over the Galois field with the arbitrary prime number p as the characteristic is obtained. Thus, the partial generation algorithm of generalized linear orthomorphism is achieved. The counting formula of the linear orthomorphism in the vector space over the finite field with characteristic 2 is the special case in our results. Furthermore, the generalized linear orthomorphism generated and discussed in this paper can gain the maximum branch number when they are designed as P-permutations.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).
基金Supported by the National Natural Science Foundation of China (60970115, 91018008)
文摘The conception of orthomorphism has been generalized in this paper, and a counting formula on the generalized linear orthomorphism in the vector space over the Galois field with the arbitrary prime number p as the characteristic is obtained. Thus, the partial generation algorithm of generalized linear orthomorphism is achieved. The counting formula of the linear orthomorphism in the vector space over the finite field with characteristic 2 is the special case in our results. Furthermore, the generalized linear orthomorphism generated and discussed in this paper can gain the maximum branch number when they are designed as P-permutations.
