End-regular flower graphs C_r,s

Authors

JOERG KOPPITZFollow
SUPARAT PHANTUKANGFollow
PHURINUT SRISAWADFollow
SOMNUEK WORAWISETFollow

Author ORCID Identifier

JOERG KOPPITZ: 0000-0001-6483-4854

SUPARAT PHANTUKANG: 0009-0005-0456-9493

PHURINUT SRISAWAD: 0009-0005-6197-1673

SOMNUEK WORAWISET: 0000-0002-4799-2743

Abstract

In the present paper, we study the regularity of the endomorphism monoid of a class of graphs, which generalizes the cycle graph. We give a complete list of all end-regular r × s flower graphs. In particular, for an odd integer s ≥ 3, the s × s flower graph Cs,s has a regular endomorphism monoid, i.e., Cs,s is end-regular. For Cs,s, s ≥ 3 odd, we determine the cardinality and the rank of its endomorphism monoid (including a generating set of minimal size).

DOI

10.55730/1300-0098.3623

Keywords

Monoid, graph endomorphisms, regularity, flower graph

First Page

755

Last Page

767

Publisher

The Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

KOPPITZ, J, PHANTUKANG, S, SRISAWAD, P, & WORAWISET, S (2025). End-regular flower graphs C_r,s. Turkish Journal of Mathematics 49 (6): 755-767. https://doi.org/10.55730/1300-0098.3623