Several features of a complete graphs and regularity graphs in the rings

Abstract

Suppose that Reg⁡(ψ(R)) and Ω(ψ(R)) have been the sub-graphs of complete graph C(ψ(R)) generated as the sets of all regularity components and nil in R. We find out when every one of the graphs C(ψ(R)), Reg⁡(ψ(R)) and Ω(ψ(R)) is linked and homogenous. Whenever Reg⁡(ψ(R)) and Ω(ψ(R)) are both Eulerian and regularity.