交换环上单位图的Wiener索引

Pub Date : 2022-04-30 DOI:10.1142/s1005386722000189

T. Asir, V. Rabikka, H. Su

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引用次数: 3

摘要

设[公式:见文]为非零单位元环。[公式:见文]的单位图，用[公式:见文]表示，是一个以[公式:见文]的所有元素为顶点的无向图，当且仅当[公式:见文]是[公式:见文]的一个单位时，不同的顶点[公式:见文]、[公式:见文]相邻。本文研究了[公式:见文]的维纳指数和超维纳指数，并明确确定了它们的值。

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 Wiener Index of Unit Graph Associated with a Commutative Ring

Let [Formula: see text] be a ring with non-zero identity. The unit graph of [Formula: see text], denoted by [Formula: see text], is an undirected graph with all the elements of [Formula: see text] as vertices and where distinct vertices [Formula: see text], [Formula: see text] are adjacent if and only if [Formula: see text] is a unit of [Formula: see text]. In this paper, we investigate the Wiener index and hyper-Wiener index of [Formula: see text] and explicitly determine their values.

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