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Unicyclic Graphs Whose Completely Regular Endomorphisms form a Monoid

Author

Listed:
  • 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)

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 .

Suggested Citation

  • Rui Gu & Hailong Hou, 2020. "Unicyclic Graphs Whose Completely Regular Endomorphisms form a Monoid," Mathematics, MDPI, vol. 8(2), pages 1-8, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:240-:d:320276
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    Cited by:

    1. Rui Gu & Hailong Hou, 2023. "Endomorphism Type of P (3 m + 1,3)," Mathematics, MDPI, vol. 11(11), pages 1-6, May.

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