The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs

A k-uniform hypergraph H = (V ;E) is called self-complementary if there is a permutation σ : V → V , called a complementing permutation, such that for every k-subset e of V , e ∈ E if and only if σ(e) ∉ E. In other words, H is isomorphic with H′ = (V ; V(k) − E). In this paper we define a bi-regular...

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Bibliographic Details
Published in:Discussiones Mathematicae Graph Theory
Main Authors: Kamble Lata N., Deshpande Charusheela M., Bam Bhagyashree Y.
Format: Article
Language:English
Published: University of Zielona Góra 2016-05-01
Subjects:
self-complementary hypergraph
uniform hypergraph
regular hypergraph
quasi regular hypergraph
bi-regular hypergraph
Online Access:https://doi.org/10.7151/dmgt.1862
Description
Summary:A k-uniform hypergraph H = (V ;E) is called self-complementary if there is a permutation σ : V → V , called a complementing permutation, such that for every k-subset e of V , e ∈ E if and only if σ(e) ∉ E. In other words, H is isomorphic with H′ = (V ; V(k) − E). In this paper we define a bi-regular hypergraph and prove that there exists a bi-regular self-complementary 3-uniform hypergraph on n vertices if and only if n is congruent to 0 or 2 modulo 4. We also prove that there exists a quasi regular self-complementary 3-uniform hypergraph on n vertices if and only if n is congruent to 0 modulo 4.
ISSN:2083-5892

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