AIMS Mathematics, Volume (6), No (10), Year (2021-1) , Pages (10395-10404)

Title : ( A bipartite graph associated to elements and cosets of subgroups of a finite group )

Authors: Saba Al-Kaseasbeh , Ahmad Erfanian ,

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Abstract

Let G be a finite group. A bipartite graph associated to elements and cosets of subgroups of G is the simple undirected graph Γ(G) with the vertex set V(Γ(G)) = A [ B, where A is the set of all elements of a group G and B is the set of all subgroups of a group G and two vertices x 2 A and H 2 B are adjacent if and only if xH = Hx. In this article, several graph theoretical properties are investigated. Also, we obtain the diameter, girth, and the dominating number of Γ(G). We discuss the planarity and outer planarity for Γ(G). Finally, we prove that if p and q are distinct prime numbers and n = pqk, where p < q and k ≥ 1, then Γ(D2n) is not Hamiltonian.

Keywords

bipartite graph; connected graph; planar graph; outer planar graph; Hamiltonian graph; finite group
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@article{paperid:1088557,
author = {Saba Al-Kaseasbeh and Erfanian, Ahmad},
title = {A bipartite graph associated to elements and cosets of subgroups of a finite group},
journal = {AIMS Mathematics},
year = {2021},
volume = {6},
number = {10},
month = {January},
issn = {2473-6988},
pages = {10395--10404},
numpages = {9},
keywords = {bipartite graph; connected graph; planar graph; outer planar graph; Hamiltonian graph; finite group},
}

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%0 Journal Article
%T A bipartite graph associated to elements and cosets of subgroups of a finite group
%A Saba Al-Kaseasbeh
%A Erfanian, Ahmad
%J AIMS Mathematics
%@ 2473-6988
%D 2021

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