Zero divisor graphs of classes of five radical zero commutative

Were, Hezron Saka; Oduor, Maurice Owino

doi:10.22075/ijnaa.2024.34289.5117

Zero divisor graphs of classes of five radical zero commutative

Articles in Press

Document Type : Research Paper

Authors

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

References

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