@article{Alluqmani2026, 
author = {Eman Alluqmani},
title = {Unit graphs of group rings},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {1},
pages = {2907-2934},
keywords = {unit graph, group ring, connectivity, diameter, cycle classification, girth},
url = {https://www.sciopen.com/article/10.3934/math.2026116},
doi = {10.3934/math.2026116},
abstract = {In this paper, we studied the unit graph    Υ  (  R  G  ) of a finite group ring    R  G, where two vertices    x  ,  y  ∈  R  G were adjacent when    x  +  y was a unit. We established algebraic criteria for connectivity, described all connected components, and determined the diameter of    Υ  (  R  G  ) in terms of the semisimple quotient    R  G      /    J  (  R  G  ). We classified completely when the unit graph was a cycle or a complete graph, and we determined the girth of    Υ  (  R  G  ) from the field factorization of the quotient. The results revealed a tight correspondence between the additive structure generated by units and the global geometry of the unit graph.}
}