Algebraic Properties of Endomorphism Monoids on Barbell Graphs

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Published: Jun 29, 2026
Keywords:
Barbell graph Graph endomorphism monoid Regular monoid Orthodox

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Bawornrat Somsri
Program of Mathematics, Faculty of Science and Technology, Kamphaeng Phet Rajabhat University
Nirutt Pipattanajinda
Program of Mathematics, Faculty of Science and Technology, Kamphaeng Phet Rajabhat University

Abstract

This research investigates the algebraic properties and characterization of the endomorphism monoid of the barbell graph Bn, formed by two complete graphs Kn joined by a bridge. We characterize the mapping properties of End(Bn) into four distinct classes End(Kn ,K'n), End(K'n ,Kn), End(Kn ,Kn), and End(K'n ,K'n), which constitute a monoid structure under the operation of function composition. Within this structure, End(Kn ,K'n) acts as the identity element, while End(Kn ,Kn) and End(K'n ,K'n) serve as right zero elements. Furthermore, we establish that End(Bn) is always a regular monoid and satisfies the orthodox monoid if and only if n ≤ 2.

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How to Cite
Somsri, B., & Pipattanajinda, N. (2026). Algebraic Properties of Endomorphism Monoids on Barbell Graphs. Journal of Science and Technology CRRU, 5(1), 33–42. retrieved from https://li01.tci-thaijo.org/index.php/jstcrru/article/view/270687
Issue
Vol. 5 No. 1 (2026): January - June
Section
Research article
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References

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