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

Monalisha Sharma, Rajat Kanti Nath, Yilun Shang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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 ΔgH,G 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 ΔgH,G is a tree among other results. We also discuss about its diameter and connectivity with special attention to the dihedral groups.
Original languageEnglish
Article number3147
Number of pages13
JournalMathematics
Volume9
Issue number23
DOIs
Publication statusPublished - 6 Dec 2021

Fingerprint

Dive into the research topics of 'On g-Noncommuting Graph of a Finite Group Relative to Its Subgroups'. Together they form a unique fingerprint.

Cite this