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

Lata N. Kamble; Charusheela M. Deshpande; Bhagyashree Y. Bam

Discussiones Mathematicae Graph Theory (2016)

  • Volume: 36, Issue: 2, page 419-426
  • ISSN: 2083-5892

Abstract

top
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.

How to cite

top

Lata N. Kamble, Charusheela M. Deshpande, and Bhagyashree Y. Bam. "The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs." Discussiones Mathematicae Graph Theory 36.2 (2016): 419-426. <http://eudml.org/doc/277125>.

@article{LataN2016,
abstract = {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.},
author = {Lata N. Kamble, Charusheela M. Deshpande, Bhagyashree Y. Bam},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {self-complementary hypergraph; uniform hypergraph; regular hypergraph; quasi regular hypergraph; bi-regular hypergraph},
language = {eng},
number = {2},
pages = {419-426},
title = {The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs},
url = {http://eudml.org/doc/277125},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Lata N. Kamble
AU - Charusheela M. Deshpande
AU - Bhagyashree Y. Bam
TI - The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 2
SP - 419
EP - 426
AB - 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.
LA - eng
KW - self-complementary hypergraph; uniform hypergraph; regular hypergraph; quasi regular hypergraph; bi-regular hypergraph
UR - http://eudml.org/doc/277125
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.