The intersection graph of finite commutative principal ideal rings

Acta Mathematica Academiae Paedagogicae Nyíregyháziensis

Emad Abu Osba¹ 

[1] University of Jordan

关键词: Eulerian graph;    Hamiltonian graph;   

DOI  :  

学科分类：数学（综合）

来源: Academia Paedagogica Nyiregyhaziensis. Acta Mathematica

【 摘 要 】

In this article we consider the intersection graph $G(R)$ of non-trivial proper ideals of a finite commutative principal ideal ring $R$ with unity $1$. Two distinct ideals are adjacent if they have non-trivial intersection. We characterize when the intersection graph is complete, bipartite, planar, Eulerian or Hamiltonian. We also find a formula to calculate the number of ideals in each ring and the degree of each ideal. We apply our results to the intersection graph of the ring of Gaussian integers modulo $n$.

【 授权许可】

Unknown