The Number of Endomorphism of Barbell Graphs

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Published: Dec 17, 2025
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Barbell graphs Endomorphisms Enumeration of endomorphisms

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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

A barbell graph equation is formed by connecting two complete graphs, namely Kn and Kn' , with a bridge. This research aims to determine the total number of endomorphisms of barbell graphs. We demonstrate that endomorphisms are divided into four distinct classes: End(Kn,Kn'), End(Kn',Kn), End(Kn,Kn) and End(Kn',Kn'). By enumerating the elements within each class, we derive a formula for the total number of endomorphisms of equation​, equation

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How to Cite
Somsri, B., & Pipattanajinda, N. (2025). The Number of Endomorphism of Barbell Graphs. Journal of Science and Technology CRRU, 4(2), 61–70. retrieved from https://li01.tci-thaijo.org/index.php/jstcrru/article/view/267592
Issue
Vol. 4 No. 2 (2025): July - December
Section
Research article
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References

Arworn, Sr. (2009). An algorithm for the numbers of endomorphisms on paths. Discrete Mathematics, 309(1), 94–103.

Arworn, Sr., & Wojtylak, P. (2009). An algorithm for the number of path homomorphisms. Discrete Mathematics, 309(17), 5569–5573.

Pipattanajinda, N. (2006). Finding the numbers of cycle homomorphisms (Master’s thesis). Chiang Mai University, Chiang Mai.

Pipattanajinda, N., & Arworn, Sr. (2010, February 22-24). Finding the number of cycle homomorphisms. In Proceedings of the International Workshop on Pure and Applied Mathematics (pp. 45–51). Chiang Mai Rajabhat University.

Hou, H., Luo, Y., & Cheng, Z. (2008). The endomorphism monoid of (P_n ) ̅. European Journal of Combinatorics, 29(5), 1173–1185.

Li, W. (2003). Graphs with regular monoid. Discrete Mathematics, 265(1-3), 105–118.

Pipattanajinda, N., Gyurov, B., & Panma, S. (2012). Path strong and cycle strong graph endomorphism and applications. Advances and Applications in Discrete Mathematics, 9(1), 29–44.

Wilkeit, A. (1996). Graphs with regular endomorphism monoid. Archiv der Mathematik, 66, 344–352.

Pipattanajinda, N., Knauer, U., Gyurov, B., & Panma, S. (2016). The endomorphism monoids of (n-3)-regular graphs of order n. Algebra and Discrete Mathematics, 22(2), 284–300.

Pipattanajinda, N., Knauer, U., Gyurov, B., & Panma, S. (2014). The endomorphism monoids of graphs of order n with minimum degree n-3. Algebra and Discrete Mathematics, 18(2), 274–294.

Hell, P., & Nešetřil, J. (2004). Graphs and homomorphisms. Oxford University Press.

Knauer, U. (2011). Algebraic graph theory: Lectures for undergraduates and graduates in mathematics and informatics. De Gruyter.

นิรุตติ์ พิพรรธนจินดา. (2560). ทฤษฎีกราฟเบื้องต้น. คณะวิทยาศาสตร์และเทคโนโลยี มหาวิทยาลัย ราชภัฏกำแพงเพชร.