End-Completely-Regular and End-Inverse Lexicographic Products of Graphs

A graph X is said to be End-completely-regular (resp., End-inverse) if its endomorphism monoid End(X) is completely regular (resp., inverse). In this paper, we will show that if X[Y] is End-completely-regular (resp., End-inverse), then both X and Y are End-completely-regular (resp., End-inverse). We...

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Detalles Bibliográficos
Autores principales: Hou, Hailong, Gu, Rui
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4032769/
https://www.ncbi.nlm.nih.gov/pubmed/24892047
http://dx.doi.org/10.1155/2014/432073
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author Hou, Hailong
Gu, Rui
author_facet Hou, Hailong
Gu, Rui
author_sort Hou, Hailong
collection PubMed
description A graph X is said to be End-completely-regular (resp., End-inverse) if its endomorphism monoid End(X) is completely regular (resp., inverse). In this paper, we will show that if X[Y] is End-completely-regular (resp., End-inverse), then both X and Y are End-completely-regular (resp., End-inverse). We give several approaches to construct new End-completely-regular graphs by means of the lexicographic products of two graphs with certain conditions. In particular, we determine the End-completely-regular and End-inverse lexicographic products of bipartite graphs.
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spelling pubmed-40327692014-06-02 End-Completely-Regular and End-Inverse Lexicographic Products of Graphs Hou, Hailong Gu, Rui ScientificWorldJournal Research Article A graph X is said to be End-completely-regular (resp., End-inverse) if its endomorphism monoid End(X) is completely regular (resp., inverse). In this paper, we will show that if X[Y] is End-completely-regular (resp., End-inverse), then both X and Y are End-completely-regular (resp., End-inverse). We give several approaches to construct new End-completely-regular graphs by means of the lexicographic products of two graphs with certain conditions. In particular, we determine the End-completely-regular and End-inverse lexicographic products of bipartite graphs. Hindawi Publishing Corporation 2014 2014-04-17 /pmc/articles/PMC4032769/ /pubmed/24892047 http://dx.doi.org/10.1155/2014/432073 Text en Copyright © 2014 H. Hou and R. Gu. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Hou, Hailong
Gu, Rui
End-Completely-Regular and End-Inverse Lexicographic Products of Graphs
title End-Completely-Regular and End-Inverse Lexicographic Products of Graphs
title_full End-Completely-Regular and End-Inverse Lexicographic Products of Graphs
title_fullStr End-Completely-Regular and End-Inverse Lexicographic Products of Graphs
title_full_unstemmed End-Completely-Regular and End-Inverse Lexicographic Products of Graphs
title_short End-Completely-Regular and End-Inverse Lexicographic Products of Graphs
title_sort end-completely-regular and end-inverse lexicographic products of graphs
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4032769/
https://www.ncbi.nlm.nih.gov/pubmed/24892047
http://dx.doi.org/10.1155/2014/432073
work_keys_str_mv AT houhailong endcompletelyregularandendinverselexicographicproductsofgraphs
AT gurui endcompletelyregularandendinverselexicographicproductsofgraphs

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