2017/05/05 by Jutirekha Dutta, Dhiren Kumar Basnet, Dutta, Jutirekha +1
Mathematics · #05C25 #16U70 #Advanced Topics in Algebra #FOS: Mathematics #Graph theory and applications #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #msc:05C25 #msc:16U70
paper · pdf · doi:10.48550/arxiv.1705.02161
9 pages
arxiv created 2017/05/05 · openalex publication_date 2017/05/05 · arxiv updated 2017/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let S be a subring of a finite ring R and CR(S) = \r ∈ R : rs = sr ∀ s ∈ S\. The relative non-commuting graph of the subring S in R, denoted by ΓS, R, is a simple undirected graph whose vertex set is R ∖ CR(S) and two distinct vertices a, b are adjacent if and only if a or b ∈ S and ab ≠ ba. In this paper, we discuss some properties of ΓS, R, determine diameter, girth, some dominating sets and chromatic index for ΓS, R. Also, we derive some connections between ΓS, R and the relative commuting probability of S in R. Finally, we show that the relative non-commuting graphs of two relative \Z-isoclinic pairs of rings are isomorphic under some conditions.