The (1, 2)-step competition graph of a hypertournament

In 2011, Factor and Merz [Discrete Appl. Math. 159 (2011), 100–103] defined the (1,2)\left(1,2)-step competition graph of a digraph. Given a digraph D=(V,A)D=\left(V,A), the (1,2)\left(1,2)-step competition graph of D, denoted C1,2(D){C}_{1,2}\left(D), is a graph on V(D)V\left(D), where xy∈E(C1,2(D)...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Li Ruijuan, An Xiaoting, Zhang Xinhong
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	k-hypertournament (1, 2)-step competition graph (i, j)-step competition graph 05c65 05c12 05c20 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/ef6a01dc546e400e873d50ec21b21afe
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:ef6a01dc546e400e873d50ec21b21afe
record_format	dspace
spelling	oai:doaj.org-article:ef6a01dc546e400e873d50ec21b21afe2021-12-05T14:10:53ZThe (1, 2)-step competition graph of a hypertournament2391-545510.1515/math-2021-0047https://doaj.org/article/ef6a01dc546e400e873d50ec21b21afe2021-06-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0047https://doaj.org/toc/2391-5455In 2011, Factor and Merz [Discrete Appl. Math. 159 (2011), 100–103] defined the (1,2)\left(1,2)-step competition graph of a digraph. Given a digraph D=(V,A)D=\left(V,A), the (1,2)\left(1,2)-step competition graph of D, denoted C1,2(D){C}_{1,2}\left(D), is a graph on V(D)V\left(D), where xy∈E(C1,2(D))xy\in E\left({C}_{1,2}\left(D)) if and only if there exists a vertex z≠x,yz\ne x,y such that either dD−y(x,z)=1{d}_{D-y}\left(x,z)=1 and dD−x(y,z)≤2{d}_{D-x}(y,z)\le 2 or dD−x(y,z)=1{d}_{D-x}(y,z)=1 and dD−y(x,z)≤2{d}_{D-y}\left(x,z)\le 2. They also characterized the (1, 2)-step competition graphs of tournaments and extended some results to the (i,j)\left(i,j)-step competition graphs of tournaments. In this paper, the definition of the (1, 2)-step competition graph of a digraph is generalized to a hypertournament and the (1, 2)-step competition graph of a k-hypertournament is characterized. Also, the results are extended to (i,j)\left(i,j)-step competition graphs of k-hypertournaments.Li RuijuanAn XiaotingZhang XinhongDe Gruyterarticlek-hypertournament(1, 2)-step competition graph(i, j)-step competition graph05c6505c1205c20MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 483-491 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	k-hypertournament (1, 2)-step competition graph (i, j)-step competition graph 05c65 05c12 05c20 Mathematics QA1-939
spellingShingle	k-hypertournament (1, 2)-step competition graph (i, j)-step competition graph 05c65 05c12 05c20 Mathematics QA1-939 Li Ruijuan An Xiaoting Zhang Xinhong The (1, 2)-step competition graph of a hypertournament
description	In 2011, Factor and Merz [Discrete Appl. Math. 159 (2011), 100–103] defined the (1,2)\left(1,2)-step competition graph of a digraph. Given a digraph D=(V,A)D=\left(V,A), the (1,2)\left(1,2)-step competition graph of D, denoted C1,2(D){C}_{1,2}\left(D), is a graph on V(D)V\left(D), where xy∈E(C1,2(D))xy\in E\left({C}_{1,2}\left(D)) if and only if there exists a vertex z≠x,yz\ne x,y such that either dD−y(x,z)=1{d}_{D-y}\left(x,z)=1 and dD−x(y,z)≤2{d}_{D-x}(y,z)\le 2 or dD−x(y,z)=1{d}_{D-x}(y,z)=1 and dD−y(x,z)≤2{d}_{D-y}\left(x,z)\le 2. They also characterized the (1, 2)-step competition graphs of tournaments and extended some results to the (i,j)\left(i,j)-step competition graphs of tournaments. In this paper, the definition of the (1, 2)-step competition graph of a digraph is generalized to a hypertournament and the (1, 2)-step competition graph of a k-hypertournament is characterized. Also, the results are extended to (i,j)\left(i,j)-step competition graphs of k-hypertournaments.
format	article
author	Li Ruijuan An Xiaoting Zhang Xinhong
author_facet	Li Ruijuan An Xiaoting Zhang Xinhong
author_sort	Li Ruijuan
title	The (1, 2)-step competition graph of a hypertournament
title_short	The (1, 2)-step competition graph of a hypertournament
title_full	The (1, 2)-step competition graph of a hypertournament
title_fullStr	The (1, 2)-step competition graph of a hypertournament
title_full_unstemmed	The (1, 2)-step competition graph of a hypertournament
title_sort	(1, 2)-step competition graph of a hypertournament
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/ef6a01dc546e400e873d50ec21b21afe
work_keys_str_mv	AT liruijuan the12stepcompetitiongraphofahypertournament AT anxiaoting the12stepcompetitiongraphofahypertournament AT zhangxinhong the12stepcompetitiongraphofahypertournament AT liruijuan 12stepcompetitiongraphofahypertournament AT anxiaoting 12stepcompetitiongraphofahypertournament AT zhangxinhong 12stepcompetitiongraphofahypertournament
_version_	1718371636106756096

The (1, 2)-step competition graph of a hypertournament

Ejemplares similares