Next Article in Journal
A Machine Learning Approach to Forecast Economic Recessions—An Italian Case Study
Next Article in Special Issue
Integral Domains in Which Every Nonzero w-Flat Ideal Is w-Invertible
Previous Article in Journal
Community Detection of Multi-Layer Attributed Networks via Penalized Alternating Factorization
Open AccessArticle

Unicyclic Graphs Whose Completely Regular Endomorphisms form a Monoid

by Rui Cu and Hailong Hou *
School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 240; https://doi.org/10.3390/math8020240
Received: 19 January 2020 / Revised: 6 February 2020 / Accepted: 6 February 2020 / Published: 13 February 2020
(This article belongs to the Special Issue Algebra and Discrete Mathematics 2020)
In this paper, completely regular endomorphisms of unicyclic graphs are explored. Let G be a unicyclic graph and let c E n d ( G ) be the set of all completely regular endomorphisms of G. The necessary and sufficient conditions under which c E n d ( G ) forms a monoid are given. It is shown that c E n d ( G ) forms a submonoid of E n d ( G ) if and only if G is an odd cycle or G = G ( n , m ) for some odd n 3 and integer m 1 .
Keywords: endomorphism; monoid; completely regular; unicyclic graph endomorphism; monoid; completely regular; unicyclic graph
MDPI and ACS Style

Cu, R.; Hou, H. Unicyclic Graphs Whose Completely Regular Endomorphisms form a Monoid. Mathematics 2020, 8, 240.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop