环 Zn 理想交点图的性质

Yelizaveta Utenko
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摘要

本文将研究环 Zn 的理想交点图的性质。理想交集图是一种简单的图,其中的顶点是环的非零理想,如果两个顶点(理想)的交集也是环的非零理想,那么这两个顶点(理想)就是相邻的。这些图可以称为等价类的交集图(见:Laxman Saha, Mithun Basak Kalishankar Tiwary "Metric dimension of ideal-intersection graph of the ring Zn" [1] )。我们还描述了环 Zn 理想交点图的最大簇。我们证明了该图的色度数等于零等价类中的元素数与元素数最多的类中的元素数之和。此外,我们还证明了偏心率等于 1 或等于 2。最后,我们描述了环 Zn 理想交点图中的中心顶点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Properties of the ideal-intersection graph of the ring Zn
In this paper we study properties of the ideal-intersection graph of the ring Zn. The graph of ideal intersections is a simple graph in which the vertices are non-zero ideals of the ring, and two vertices (ideals) are adjacent if their intersection is also a non-zero ideal of the ring. These graphs can be referred to as the intersection scheme of equivalence classes (See: Laxman Saha, Mithun Basak Kalishankar Tiwary “Metric dimension of ideal-intersection graph of the ring Zn” [1] ).In this article we prove that the triameter of graph is equal to six or less than six. We also describe maximal clique of the ideal-intersection graph of the ring Zn. We prove that the chromatic number of this graph is equal to the sum of the number of elements in the zero equivalence class and the class with the largest number of element. In addition, we demonstrate that eccentricity is equal to 1 or it is equal to 2. And in the end we describe the central vertices in the ideal-intersection graph of the ring Zn.
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