On the Idempotent Graph of Matrix Ring
Combinatorics
2024-02-20 v1
Abstract
Let F be a finite field and R = M2(F) be 2x2 matrix ring over F. In this paper, we explicitly determine all the idempotents in R. Using these idempotents, we study the idempotent graph of R whose vertex set is the set of non-trivial idempotents in R and two idempotents e, f are adjacent if ef = 0 or fe = 0. It is proved that the idempotent graph of R is connected regular graph with diameter 2. Its girth is also characterized. Further, we determine the Wiener and Harary index of the idempotent graph of R.
Cite
@article{arxiv.2402.11256,
title = {On the Idempotent Graph of Matrix Ring},
author = {Avinash Patil and P. S. Momale and C. M. Jadhav},
journal= {arXiv preprint arXiv:2402.11256},
year = {2024}
}
Comments
13 pages, 1 figure