On g-Noncommuting Graph of a Finite Group Relative to Its Subgroups

Autor: Monalisha Sharma, Rajat Kanti Nath, Yilun Shang
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: Mathematics, Vol 9, Iss 23, p 3147 (2021)
Druh dokumentu: article
ISSN: 2227-7390
DOI: 10.3390/math9233147
Popis: Let H be a subgroup of a finite non-abelian group G and g∈G. Let Z(H,G)={x∈H:xy=yx,∀y∈G}. We introduce the graph ΔH,Gg whose vertex set is G\Z(H,G) and two distinct vertices x and y are adjacent if x∈H or y∈H and [x,y]≠g,g−1, where [x,y]=x−1y−1xy. In this paper, we determine whether ΔH,Gg is a tree among other results. We also discuss about its diameter and connectivity with special attention to the dihedral groups.
Databáze: Directory of Open Access Journals
Externí odkaz:
Nepřihlášeným uživatelům se plný text nezobrazuje