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All Journal Journal of the Indonesian Mathematical Society
Nur Idayu Alimon
Mathematical Sciences Studies, Universiti Teknologi MARA Johor Branch
Mathematics

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The Non-Normal Cyclic Subgroup Graph Associated with Quasidihedral Groups of Order 16 Nur Nabilah Abdul Razak; Nur Idayu Alimon; Adem Kilicman; Nor Haniza Sarmin; Nabilah Fikriah Rahin; I Gede Adhitya Wisnu Wardhana
Journal of the Indonesian Mathematical Society Vol. 32 No. 3 (2026): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i3.2140

Abstract

Let \textsl{G} be a group and \textsl{H} be a non-normal cyclic subgroup of \textsl{G}. The non-normal cyclic subgroup graph, denoted as $\Gamma^{NN}_{H}(G)$, is defined as a directed graph with vertex set elements of \textsl{G} such that for two distinct elements \textsl{x} and \textsl{y} in \textsl{G}, \textsl{x} is the initial vertex and \textsl{y} is the terminal vertex of an edge if their product is in \textsl{H}. In 2020, the idea of the non-normal subgroup graph, which is the extension of the subgroup graph was developed. This research identifies the non-normal cyclic subgroup graphs connected to order 16 quasidihedral groups. Firstly, the Groups, Algorithms and Programming (GAP) software is used to identify the non-normal cyclic subgroups. The definition of $\Gamma^{NN}_{H}(G)$ is then used to calculate the adjacency and direction of the vertices. Lastly, Maple 2016 software will be used to visualize these graphs.
Co-Authors Adem Kilicman I Gede Adhitya Wisnu Wardhana Nabilah Fikriah Rahin Nor Haniza Sarmin Nur Nabilah Abdul Razak