✦ LIBER ✦

Constructing regular self-complementary uniform hypergraphs

✍ Scribed by Shonda Gosselin

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 181 KB
Volume: 19
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20286

No coin nor oath required. For personal study only.

✦ Synopsis

In this article, we examine the possible orders of t-subset-regular selfcomplementary k-uniform hypergraphs, which form examples of large sets of two isomorphic t-designs. We reformulate Khosrovshahi and Tayfeh-Rezaie's necessary conditions on the order of these structures in terms of the binary representation of the rank k, and these conditions simplify to a more transparent relation between the order n and rank k in the case where k is a sum of consecutive powers of 2. Moreover, we present new constructions for 1-subset-regular self-complementary uniform hypergraphs, and prove that these necessary conditions are sufficient for all k, in the case where t = 1.

📜 SIMILAR VOLUMES

On regular self-complementary graphs

✍ Nora Hartsfield 📂 Article 📅 1987 🏛 John Wiley and Sons 🌐 English ⚖ 74 KB

A regular self-complementary graph is presented which has no complementing permutation consisting solely of cycles of length four. This answers one of Kotzig's questions.

On strongly regular self - complementary

On strongly regular self - complementary graphs

✍ Sergio Ruiz 📂 Article 📅 1981 🏛 John Wiley and Sons 🌐 English ⚖ 133 KB 👁 1 views

## Abstract It is shown that certain conditions assumed on a regular self‐complementary graph are not sufficient for the graph to be strongly regular, answering in the negative a question posed by Kotzig in [1].

Constructions of Self-complementary Circ

Constructions of Self-complementary Circulants with No Multiplicative Isomorphisms

✍ Robert Jajcay; Cai Heng Li 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 124 KB

The main topic of the paper is the question of the existence of self-complementary Cayley graphs Cay(G, S) with the property S σ = G # \ S for all σ ∈ Aut(G). We answer this question in the positive by constructing an infinite family of self-complementary circulants with this property. Moreover, we