dc.contributor.author | Gosselin, Shonda | |
dc.date.accessioned | 2010-12-17T20:39:35Z | |
dc.date.available | 2010-12-17T20:39:35Z | |
dc.date.issued | 2009-09 | |
dc.identifier.citation | Gosselin, Shonda. "Vertex-transitive self-complementary uniform hypergraphs of prime order." Discrete Mathematics 310(4) (28 February 2010): 671-680. DOI: 10.1016/j.disc.2009.08.011. | |
dc.identifier.uri | http://hdl.handle.net/10680/295 | |
dc.description.abstract | For an integer n and a prime p, let n(p)=max{i:pidividesn}. In this paper, we present a construction for vertex-transitive self-complementary k-uniform hypergraphs of order n for each integer n such that pn(p)≡1(mod2ℓ+1) for every prime p, where ℓ=max{k(2),(k−1)(2)}, and consequently we prove that the necessary conditions on the order of vertex-transitive self-complementary uniform hypergraphs of rank k=2ℓ or k=2ℓ+1 due to Potoňick and Šajna are sufficient. In addition, we use Burnside’s characterization of transitive groups of prime degree to characterize the structure of vertex-transitive self-complementary k-hypergraphs which have prime order p in the case where k=2ℓ or k=2ℓ+1 and p≡1(mod2ℓ+1), and we present an algorithm to generate all of these structures. We obtain a bound on the number of distinct vertex-transitive self-complementary graphs of prime order p≡1(mod4), up to isomorphism. | en_US |
dc.description.sponsorship | University of Winnipeg | en_US |
dc.description.uri | https://www.sciencedirect.com/science/article/pii/S0012365X09004051?via%3Dihub | |
dc.language.iso | en | en_US |
dc.publisher | Discrete Mathematics | en_US |
dc.rights | info:eu-repo/semantics/openAccess | |
dc.subject | Self-complementary graphs | en_US |
dc.subject | Uniform hypergraphs | en_US |
dc.subject | Transitive hypergraphs | en_US |
dc.subject | Complementing permutation | en_US |
dc.title | Vertex-transitive self-complementary uniform hypergraphs of prime order | en_US |
dc.type | Article | en_US |
dc.type | Research Paper | en_US |
dc.description.version | This is an author-produced, peer-reviewed article that has been accepted for publication in Discrete Mathematics, but has not been copy-edited. | |
dc.identifier.doi | 10.1016/j.disc.2009.08.011 | |