Zero divisor graphs of skew Hurwitz series rings

Abstract

For a ring endomorphism $\alpha$, we investigate the
interplay between the ring-theoretical properties of the skew
Hurwitz series ring $(HR, \alpha )$ and the graph-theoretical
properties of its zero-divisor graph $\overline{\Gamma}((HR, \alpha
))$. Furthermore, we examine the preservation of diameter and girth
of the zero-divisor graph under extension to skew Hurwitz series
rings.