Unicyclic Graphs Whose Completely Regular Endomorphisms form a Monoid

Rui Gu and Hailong Hou
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Rui Gu: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
Hailong Hou: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China

Mathematics, 2020, vol. 8, issue 2, 1-8

Abstract: 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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