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All Journal Journal of the Indonesian Mathematical Society
Yeni Susanti
Universitas Gadjah Mada
Mathematics

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THE NON-BRAID GRAPH OF DIHEDRAL GROUP Dn Hubbi Muhammad; Rambu Maya Imung Maharani; Sri Nurhayati; Mira Wadu; Yeni Susanti
Journal of the Indonesian Mathematical Society VOLUME 30 NUMBER 1 (MARCH 2024)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.1.1401.110-120

Abstract

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
Co-Authors Hubbi Muhammad Mira Wadu Rambu Maya Imung Maharani Sri Nurhayati