1. bookAHEAD OF PRINT
Journal Details
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Format
Journal
eISSN
2083-5892
First Published
13 Apr 2013
Publication timeframe
4 times per year
Languages
English
access type Open Access

Extending Potočnik and Šajna’s Conditions on the Existence of Vertex-Transitive Self-Complementary k-Hypergraphs

Published Online: 20 Oct 2020
Volume & Issue: AHEAD OF PRINT
Page range: -
Received: 11 Mar 2020
Accepted: 02 Sep 2020
Journal Details
License
Format
Journal
eISSN
2083-5892
First Published
13 Apr 2013
Publication timeframe
4 times per year
Languages
English
Abstract

Let be a positive integer, k = 2 or k = 2 + 1, and let n be a positive integer with n ≡ 1 (mod 2ℓ+1). For a prime p, n(p) denotes the largest integer i such that pi divides n. Potočnik and Šajna showed that if there exists a vertex-transitive self-complementary k-hypergraph of order n, then for every prime p we have pn(p) ≡ 1 (mod 2ℓ+1). Here we extend their result to a larger class of integers k.

Keywords

MSC 2010

[1] R.A. Beezer, Sylow subgraphs in self-complementary vertex transitive graphs, Expo. Math. 24 (2006) 185–194. doi:10.1016/j.exmath.2005.09.00310.1016/j.exmath.2005.09.003Search in Google Scholar

[2] M. Muzychuk, On Sylow subgraphs of vertex-transitive self-complementary graphs, Bull. Lond. Math. Soc. 31 (1999) 531–533. doi:10.1112/S002460939900592510.1112/S0024609399005925Search in Google Scholar

[3] S. Gosselin, Vertex-transitive self-complementary uniform hypergraphs of prime order, Discrete Math. 310 (2010) 671–680. doi:10.1016/j.disc.2009.08.01110.1016/j.disc.2009.08.011Search in Google Scholar

[4] W.K. Nicholson, Introduction to Abstract Algebra (Wiley-Interscience, 2007).Search in Google Scholar

[5] P. Potočnik and M. Šajna, Vetrex-transitive self-complementary uniform hyper-graphs, European J. Combin. 28 (2009) 327–337. doi:10.1016/j.ejc.2007.08.00310.1016/j.ejc.2007.08.003Search in Google Scholar

[6] S.B. Rao, On regular and strongly-regular self-complementary graphs, Discrete Math. 54 (1985) 73–82. doi:10.1016/0012-365X(85)90063-910.1016/0012-365X(85)90063-9Search in Google Scholar

[7] A. Szymański and A.P. Wojda, Self-complementing permutations of k-uniform hypergraphs, Discrete Math. Theor. Comput. Sci. 11 (2009) 117–124.Search in Google Scholar

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