Idempotent Cayley Graph of the Ring (Z_n,⊕,⊙)

Authors

  • Madhavi Levaku Department of Applied Mathematics, Yogi Vemana University, Kadapa
  • Seetaka Anand Department of Applied Mathematics, Yogi Vemana University, Kadapa
  • Ramya Thejeswini Department of Applied Mathematics, Yogi Vemana University, Kadapa

DOI:

https://doi.org/10.14738/aivp.1305.19467

Keywords:

Idempotent element, idempotent Cayley graph, connected, bipartite, Hamiltonian.

Abstract

The idempotent Cayley graph of the ring  is the Cayley graph associated with the symmetric set consisting of idempotent elements and their inverses in the group . In this paper, we derive some basic properties of the idempotent elements and construct the idempotent Cayley graph. It is shown that this graph is connected and Hamiltonian. Further, if , this graph is bipartite.

Author Biographies

Seetaka Anand, Department of Applied Mathematics, Yogi Vemana University, Kadapa

Project Fellow (RUSA 2.0) and Research Scholar, Department of Applied Mathematics, Yogi Vemana University, Kadapa.

Ramya Thejeswini, Department of Applied Mathematics, Yogi Vemana University, Kadapa

Research Scholar, Department of Applied Mathematics, Yogi Vemana University, Kadapa.

References

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Published

2025-10-12

How to Cite

Levaku, M., Anand, S., & Thejeswini, R. (2025). Idempotent Cayley Graph of the Ring (Z_n,⊕,⊙). European Journal of Applied Sciences, 13(05), 278–286. https://doi.org/10.14738/aivp.1305.19467

Issue

Vol. 13 No. 05 (2025): European Journal of Applied Sciences

Section

Articles

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Copyright (c) 2025 Madhavi Levaku, Seetaka Anand, Ramya Thejeswini

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