A Kind of Intersection Graphs on Ideals of a Ring
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.
DOI: https://doi.org/10.3844/jmssp.2012.82.84
Copyright: © 2012 A. A. Talebi. This is an open access article distributed under the terms of the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Keywords
- Graphs related
- intersection graph
- integers modulo
- algebraic structure
- distinct vertices
- intersection graphs
- obtain conditions