On compressed zero divisor graphs associated to the ring of integers modulo n

Authors

  • M. Aijaz University of Kashmir, 190006, Srinagar, Kashmir, India
  • K. Rani Lovely Professional University, 144411, Punjab, India
  • S. Pirzada University of Kashmir, 190006, Srinagar, Kashmir, India https://orcid.org/0000-0002-1137-517X
https://doi.org/10.15330/cmp.15.2.552-558

Keywords:

ring, compressed zero divisor graph, coloring, clique number
Published online: 2023-12-26

Abstract

Let R be a commutative ring with unity 10. In this paper, we completely describe the vertex and the edge chromatic number of the compressed zero divisor graph of the ring of integers modulo n. We find the clique number of the compressed zero divisor graph ΓE(Zn) of Zn and show that ΓE(Zn) is weakly perfect. We also show that the edge chromatic number of ΓE(Zn) is equal to the largest degree proving that ΓE(Zn) resides in class 1 family of graphs.

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Aijaz, M.; Rani, K.; Pirzada, S. On Compressed Zero Divisor Graphs Associated to the Ring of Integers Modulo n. Carpathian Math. Publ. 2023, 15, 552-558.