Research Article Open Access

A Kind of Intersection Graphs on Ideals of a Ring

A. A. Talebi

Abstract

Problem statement: Let R be a ring. The graph G(R) is the graph whose vertices are nontrivial ideal of R and in which two vertices u, v are joined by an edge, if and only if u ∩ v #{0}. Approach: In this study we study some properties of G(R). Results: We obtain conditions of R such that G(R) is a path and determine the graph G(R) in which it is a tree. Conclusion: We conclude that ideals of R have degree one.

Journal of Mathematics and Statistics
Volume 8 No. 1, 2012, 82-84

DOI: https://doi.org/10.3844/jmssp.2012.82.84

Submitted On: 3 June 2011 Published On: 6 February 2012

How to Cite: Talebi, A. A. (2012). A Kind of Intersection Graphs on Ideals of a Ring. Journal of Mathematics and Statistics, 8(1), 82-84. https://doi.org/10.3844/jmssp.2012.82.84

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Keywords

  • Graphs related
  • intersection graph
  • integers modulo
  • algebraic structure
  • distinct vertices
  • intersection graphs
  • obtain conditions