Abstract
Let R be a noncommutative ring with unity and be its centre. The commuting graph of R denoted by
is a graph whose vertices are noncentral elements of R and two distinct vertices x and y are adjacent if and only if xy = yx. Let F be a finite field. In this paper, we show that if
and
is a field, then
. In particular, if
, then
.
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Acknowledgments
The authors would like to express their deep gratitude to referees for a very careful reading of the paper, and many valuable comments which have greatly improved the presentation of the paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Correction Statement
This article has been corrected with minor changes. These changes do not impact the academic content of the article.