- Hacettepe Journal of Mathematics and Statistics
- Vol: 49 Issue: 2
- Ideal based trace graph of matrices
Ideal based trace graph of matrices
Authors : Tamizh Chelvam Thirugnanam, M. Sivagami
Pages : 608-616
Doi:10.15672/hujms.478373
View : 12 | Download : 4
Publication Date : 2020-04-02
Article Type : Research
Abstract :Let $R$ be a commutative ring and $M_n(R)$ be the set of all $n\times n$ matrices over $R$ where $n\geq 2.$ The trace graph of the matrix ring $M_n(R)$ with respect to an ideal $I$ of $R,$ denoted by $\Gamma_{I^t}(M_n(R)),$ is the simple undirected graph with vertex set $M_n(R)\setminus M_n(I)$ and two distinct vertices $A$ and $B$ are adjacent if and only if Tr$(AB) \in I.$ Here Tr$(A)$ represents the trace of the matrix $A.$ In this paper, we exhibit some properties and structure of $\Gamma_{I^t}(M_n(R)).$Keywords : Trace graph, Matrix ring, Ideal based graph, clique number