A Kind of Intersection Graphs on Ideals of a Ring | Science Publications

Journal of Mathematics and Statistics

A. A. Talebi¹ 

关键词: Graphs related;    intersection graph;    integers modulo;    algebraic structure;    distinct vertices;    intersection graphs;    obtain conditions;   

DOI  :  10.3844/jmssp.2012.82.84

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

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.

【 授权许可】

Unknown