The intersection graph of finite commutative principal ideal rings

Osba, Emad Abu (2016) The intersection graph of finite commutative principal ideal rings. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 32 (1). pp. 15-22. ISSN 0866-0174

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Abstract

In this article we consider the intersection graph G(R) of nontrivial 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.

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