@article{Moh'd2023, 
author = {Fida Moh'd and Mamoon Ahmed},
title = {Simple-intersection graphs of rings},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {1},
pages = {1040-1054},
keywords = {simple-intersection graph, rings, ideals, clique, girth, dominating number, cycles, diameter, connected graph, complete graph},
url = {https://www.sciopen.com/article/10.3934/math.2023051},
doi = {10.3934/math.2023051},
abstract = {Let    R be a ring with unity. In this paper, we introduce a new graph associated with    R called the simple-intersection graph of    R, denoted by    G  S  (  R  ). The vertices of    G  S  (  R  ) are the nonzero ideals of    R, and two vertices are adjacent if and only if their intersection is a nonzero simple ideal. We study the interplay between the algebraic properties of    R, and the graph properties of    G  S  (  R  ) such as connectedness, bipartiteness, girth, dominating sets, etc. Moreover, we determine the precise values of the girth and diameter of    G  S  (  R  ), as well as give a formula to compute the clique and domination numbers of    G  S  (  R  ).}
}