Name
Abstract | ||
|---|---|---|
Let R be a finite ring and r is an element of R. The r-noncommuting graph of R, denoted by Gamma(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] not equal r and [x,y] not equal -r. In this paper, we obtain expressions for vertex degrees and show that Gamma Rr is neither a regular graph nor a lollipop graph if R is noncommutative. We characterize finite noncommutative rings such that Gamma(r)(R) is a tree, in particular a star graph. It is also shown that Gamma(r)(R1) and Gamma(2 psi)(R) (r) are isomorphic if R-1 and R-2 are two isoclinic rings with isoclinism (phi,psi). Further, we consider the induced subgraph Delta(r)(R) of Gamma(r)(R) (induced by the non-central elements of R) and obtain results on clique number and diameter of Delta(r)(R) along with certain characterizations of finite noncommutative rings such that Delta(r)(R) is n-regular for some positive integer n. As applications of our results, we characterize certain finite noncommutative rings such that their noncommuting graphs are n-regular for n <= 6. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.3390/axioms10030233 | AXIOMS |
Keywords | DocType | Volume |
finite ring, noncommuting graph, isoclinism | Journal | 10 |
Issue | Citations | PageRank |
3 | 0 | 0.34 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rajat Kanti Nath | 1 | 0 | 0.34 |
| Monalisha Sharma | 2 | 0 | 0.34 |
| Parama Dutta | 3 | 0 | 0.34 |
| Yilun Shang | 4 | 16 | 6.99 |