In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine theisomorphic classes of circulant digraphs of degree 3. In particul...In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine theisomorphic classes of circulant digraphs of degree 3. In particular, we characterizethose circulant digraphs of degree 3 which don't satisfy Adam's conjecture.展开更多
A Cayley graph F = Cay（G, S） of a group G with respect to S is called a circulant digraph of order pk if G is a cyclic group of the same order. Investigated in this paper are the normality conditions for arc-transit...A Cayley graph F = Cay（G, S） of a group G with respect to S is called a circulant digraph of order pk if G is a cyclic group of the same order. Investigated in this paper are the normality conditions for arc-transitive circulant （di）graphs of order p^2 and the classification of all such graphs. It is proved that any connected arc-transitive circulant digraph of order p^2 is, up to a graph isomorphism, either Kp2, G（p^2,r）, or G（p,r）[pK1], where r｜p- 1.展开更多
Some researchers have proved that Adam＇s conjecture is wrong. However, under special conditions,it is right. Let Zn be a cyclic group of order n and Cn（S） be the circulant digraph of Zn with respect to S？Zn／{0}. ...Some researchers have proved that Adam＇s conjecture is wrong. However, under special conditions,it is right. Let Zn be a cyclic group of order n and Cn（S） be the circulant digraph of Zn with respect to S？Zn／{0}. In the literature, some people have used a spectral method to solve the isomorphism for the circulants of prime-power order. In this paper, we also use the spectral method to characterize the circulants of order paqbωc（where p,q and ω are all distinct primes）, and to make Adam＇s conjecture right.展开更多
In this paper, we completely determine the connectivity of every infinite circulant digraphs and prove that almost all infinite circulant digraphs are infinitely strongly connected and therefore have both one-and two-...In this paper, we completely determine the connectivity of every infinite circulant digraphs and prove that almost all infinite circulant digraphs are infinitely strongly connected and therefore have both one-and two-way infinite Hamiltonian paths.展开更多
基金Supported by the National Natural Science Foundation of China.
文摘In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine theisomorphic classes of circulant digraphs of degree 3. In particular, we characterizethose circulant digraphs of degree 3 which don't satisfy Adam's conjecture.
基金Research supported by the National Natural Science Foundation of China under Grant No.103710003
文摘A Cayley graph F = Cay（G, S） of a group G with respect to S is called a circulant digraph of order pk if G is a cyclic group of the same order. Investigated in this paper are the normality conditions for arc-transitive circulant （di）graphs of order p^2 and the classification of all such graphs. It is proved that any connected arc-transitive circulant digraph of order p^2 is, up to a graph isomorphism, either Kp2, G（p^2,r）, or G（p,r）[pK1], where r｜p- 1.
基金supported by Start high-level personnel of scientific research funds of Jiangsu Second Normal University(No.918001)NSFC(11171283)
文摘Some researchers have proved that Adam＇s conjecture is wrong. However, under special conditions,it is right. Let Zn be a cyclic group of order n and Cn（S） be the circulant digraph of Zn with respect to S？Zn／{0}. In the literature, some people have used a spectral method to solve the isomorphism for the circulants of prime-power order. In this paper, we also use the spectral method to characterize the circulants of order paqbωc（where p,q and ω are all distinct primes）, and to make Adam＇s conjecture right.
基金Supported by Natural Science Foundation of China (Project 10171085).
文摘In this paper, we completely determine the connectivity of every infinite circulant digraphs and prove that almost all infinite circulant digraphs are infinitely strongly connected and therefore have both one-and two-way infinite Hamiltonian paths.
