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...

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Published inJournal of the Indonesian Mathematical Society pp. 110 - 120
Main Authors Muhammad, Hubbi, Maharani, Rambu Maya Imung, Nurhayati, Sri, Wadu, Mira, Susanti, Yeni
Format Journal Article
LanguageEnglish
Published 14.05.2024
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Summary: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
ISSN:2086-8952
2460-0245
DOI:10.22342/jims.30.1.1401.110-120