交换环的强湮灭理想图的度规维数

Pub Date : 2020-11-01 DOI:10.2478/ausm-2020-0025

V. Soleymanivarniab, R. Nikandish, A. Tehranian

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引用次数: 0

摘要

设𝒭是一个具有恒等式的交换环，且𝒭是具有非零湮灭子的理想集合。定义了𝒭的强湮灭理想图SAG(𝒭)，其顶点集为:(𝒭)* =(𝒭)\{0}，且两个不同的顶点I和J相邻当且仅当I∩Ann(J)≠(0)且J∩Ann(I)≠(0)。本文研究了SAG(𝒭)的度量维数，并给出了一些强湮灭理想图的度量维数公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the metric dimension of strongly annihilating-ideal graphs of commutative rings

Abstract Let 𝒭 be a commutative ring with identity and 𝒜(𝒭) be the set of ideals with non-zero annihilator. The strongly annihilating-ideal graph of 𝒭 is defined as the graph SAG(𝒭) with the vertex set 𝒜 (𝒭)* = 𝒜 (𝒭) \{0} and two distinct vertices I and J are adjacent if and only if I ∩ Ann(J) ≠ (0) and J ∩ Ann(I) ≠ (0). In this paper, we study the metric dimension of SAG(𝒭) and some metric dimension formulae for strongly annihilating-ideal graphs are given.

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