与以n为模的整数环相关的协单位图

Pub Date : 2022-12-01 DOI:10.2478/ausm-2022-0020

S. Pirzada, Aaqib Altaf

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引用次数: 0

摘要

设R是一个有限交换环。定义一个与环R相关的共单位图，记作Gnu(R)，其顶点集V(Gnu(R)) = U(R)，其中U(R)是R的单位集合，且U(R)的两个不同的顶点x, y相邻当且仅当x + y∈U(R)。本文研究了不同n值下Gnu(R)的一些基本性质，其中R是模为n的整数环，得到了Gnu(R)的支配数、团数和周长。

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Co-unit graphs associated to ring of integers modulo n

Abstract Let R be a finite commutative ring. We define a co-unit graph, associated to a ring R, denoted by Gnu(R) with vertex set V(Gnu(R)) = U(R), where U(R) is the set of units of R, and two distinct vertices x, y of U(R) being adjacent if and only if x + y ∉ / U(R). In this paper, we investigate some basic properties of Gnu(R), where R is the ring of integers modulo n, for different values of n. We find the domination number, clique number and the girth of Gnu(R).

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