Vertex-transitive self-complementary uniform hypergraphs of prime order
نویسندگان
چکیده
منابع مشابه
Vertex-transitive self-complementary uniform hypergraphs
In this paper we examine the orders of vertex-transitive self-complementary uniform hypergraphs. In particular, we prove that if there exists a vertex-transitive selfcomplementary k-uniform hypergraph of order n, where k = 2 or k = 2 + 1 and n ≡ 1 (mod 2), then the highest power of any prime dividing n must be congruent to 1 modulo 2. We show that this necessary condition is also sufficient in ...
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For a positive integer q, a k-uniform hypergraph X = (V,E) is q-complementary if there exists a permutation θ on V such that the sets E,E, E 2 , . . . , E q−1 partition the set of k-subsets of V . The permutation θ is called a q-antimorphism of X. The well studied self-complementary uniform hypergraphs are 2-complementary. For an integer n and a prime p, let n(p) = max{i : p i divides n}. In th...
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A graph Γ is self-complementary if its complement is isomorphic to the graph itself. An isomorphism that maps Γ to its complement Γ is called a complementing isomorphism. The majority of this dissertation is intended to present my research results on the study of self-complementary vertex-transitive graphs. I will provide an introductory mini-course for the backgrounds, and then discuss four pr...
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A k-uniform hypergraph with vertex set V and edge set E is called t-subset-regular if every t-element subset of V lies in the same number of elements of E. In this paper we establish a necessary condition on n for there to exist a t-subset-regular selfcomplementary k-uniform hypergraph with n vertices. In addition, we show that this necessary condition is also sufficient in the case k = 3 and t...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.08.011