Zero divisor graphs of classes of five radical zero commutative

Articles in Press

Document Type : Research Paper

Authors
Hezron Saka Were 1
Maurice Owino Oduor 2
1 Department of Mathematics, Egerton University, P.O. Box 536-20115, Egerton, Kenya
2 Department of Mathematics, Actuarial and Physical Sciences, University of Kabianga, P.O. Box 2030-20200, Kericho, Kenya
10.22075/ijnaa.2024.34289.5117
Abstract
This paper provides a characterization for zero divisor graphs of a completely primary finite ring $R$ satisfying the conditions $\left(Z\left(R\right)\right)^5=\left(0\right); \left(Z\left(R\right)\right)^4\neq \left(0\right)$ where $Z(R)$ is its subset of all zero divisors (including zero). This has been achieved through Anderson and Livingston's zero divisor graphs by precisely determining the graph invariants, including diameter, girth and the binding number, and graph characteristics including completeness, connectedness and partiteness.
Keywords
Completely Primary Finite Ring
Five Radical Zero
Zero Divisor Graphs
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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 22 August 2025

  • Receive Date 30 May 2024
  • Revise Date 24 August 2024
  • Accept Date 26 September 2024