On r-noncommuting graph of finite rings

2019/07/24 by Rajat Kanti Nath, Nath, Rajat Kanti, Monalisha Sharma +5
Mathematics · #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.1907.10350

17 pages

arxiv created 2021/08/20 · arxiv updated 2021/08/23

Abstract

Let R be a finite ring and r∈ R. The r-noncommuting graph of R, denoted by Γ_R^r, is a simple undirected graph whose vertex set is R and two vertices x and y are adjacent if and only if [x,y] ≠ r and -r. In this paper, we study several properties of Γ_R^r. We show that Γ_R^r is not a regular graph, a lollipop graph and complete bipartite graph. Further, we consider an induced subgraph of Γ_R^r (induced by the non-central elements of R) and obtained some characterizations of R.

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