钝化组的非线性图 Dn

IF 0.3 Q4 MATHEMATICS Journal of the Indonesian Mathematical Society Pub Date : 2024-05-14 DOI:10.22342/jims.30.1.1401.110-120

Hubbi Muhammad, Rambu Maya Imung Maharani, Sri Nurhayati, Mira Wadu, Yeni Susanti

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摘要

我们将群 G 的无辫图（用 ζ(G)表示）引入为具有顶点集 G\ B(G) 的图，其中 B(G) 是 G 的辫图，定义为集合 {x∈G | (∀y∈G)xyx = yxy}，并且当且仅当 xyx ̸ = yxy 时，两个不同的顶点 x 和 y 通过边连接。本文特别给出了二面角组 Dn 的非辫子图的独立数、顶点色度数、小群数和最小顶点覆盖率。

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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THE NON-BRAID GRAPH OF DIHEDRAL GROUP Dn

We introduce the non-braid graph of a group G, denoted by ζ(G), as a graph with vertex set G \ B(G), where B(G) is the braider of G, defined as the set {x ∈ G | (∀y ∈ G)xyx = yxy}, and two distinct vertices x and y are joined by an edge if and only if xyx ̸ = yxy. In this paper particularly we give the independent number, the vertex chromatic number, the clique number, and the minimum vertex cover of non-braid graph of dihedral group Dn

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