Sum Ideal Graphs Associated to a Given Ideal of a Commutative Ring

  • A. H. Nadir Department of Mathematics, College of Education, University of Salahaddin, Erbil, Iraq
  • F. H. Abdulqadr Department of Mathematics, College of Computer Science and Mathematics, Mosul University, Mosul, Iraq
  • N. H. Shuker Department of Mathematics, College of Computer Science and Mathematics, Mosul University, Mosul, Iraq
Keywords: Sum ideal graphs, Maximal ideals, Connected graphs

Abstract

The aim of this paper is to introduce and study a new kind of graphs associated to an ideal of a commutative ring. Let â„› be a commutative ring with identity, and I(â„›) be the set of all non-trivial ideals of â„› with S I(â„›). The sum ideal graph associated to S, denoted by       Î¨(â„›, S), is the undirected graph with vertex set {A I(â„›): S⊂A+B, for some B I(â„›)} where two ideal vertices A and B are adjacent if and only if A B and S⊂A+B. In this paper we establish some of characterizations and results of this kind of graph with providing some examples.

Published
2019-11-27
How to Cite
Nadir, A. H., Abdulqadr, F. H., & Shuker, N. H. (2019). Sum Ideal Graphs Associated to a Given Ideal of a Commutative Ring. Iraqi Journal of Science, 60(11), 2478-2485. https://doi.org/10.24996/ijs.2019.60.11.19
Section
Mathematics