Alhubairah, Fozaiyah Ayed and Mohd. Ali, Nor Muhainiah and Erfanian, Ahmad
(2023)
*Cyclic intersection graph of subgroups of dihedral groups and its properties.*
International Journal of Mathematics and Computer Science, 18
(4).
pp. 661-674.
ISSN 1814-0424

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283kB |

Official URL: http://ijmcs.future-in-tech.net/18.4/R-Alhubairah....

## Abstract

Various characteristics of the algebraic structures can be expressed by associating it to the graphs of different groups. In an intersection graph, each vertex conforms to a set wherein two vertices are connected by an edge if and only if their corresponding sets have a non-empty intersection. For a finite group G, a graph of its subgroups can be represented by the vertices that correspond to the subgroups of G. Based on this factor, we defined the cyclic intersection graph of the subgroups of a group G. The cyclic intersection graph of the subgroups of a group G enclosed all the nontrivial subgroups as its vertices together with two adjacent vertices H and K if and only if H intersection K corresponded to a non-trivial cyclic subgroup. Furthermore, the general presentation of the graph on the dihedral groups was obtained. The cyclic intersection graph of the subgroups on dihedral groups is classified as connected or planar. Additionally, some of the invariants of the the cyclic intersection graph of the subgroups on the dihedral groups are given.

Item Type: | Article |
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Uncontrolled Keywords: | cyclic intersection graph; graph invariant; Intersection graph; non-trivial subgroup. |

Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |

Divisions: | Science |

ID Code: | 105801 |

Deposited By: | Muhamad Idham Sulong |

Deposited On: | 18 May 2024 01:48 |

Last Modified: | 18 May 2024 01:48 |

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