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Properties of the ideal-intersection graph of the ring Zn
(2023) Utenko, Yelizaveta
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.