Ideal based trace graph of matrices

Authors : Tamizh Chelvam THİRUGNANAM, M. SİVAGAMİ

Pages : 608-616

Doi:10.15672/hujms.478373

View : 17 | Download : 5

Publication Date : 2020-04-02

Article Type : Research Paper

Abstract :Let $R$ be a commutative ring and $M_ninsert ignore into journalissuearticles values(R);$ be the set of all $n\times n$ matrices over $R$ where $n\geq 2.$ The trace graph of the matrix ring $M_ninsert ignore into journalissuearticles values(R);$ with respect to an ideal $I$ of $R,$ denoted by $\Gamma_{I^t}insert ignore into journalissuearticles values(M_ninsert ignore into journalissuearticles values(R););,$ is the simple undirected graph with vertex set $M_ninsert ignore into journalissuearticles values(R);\setminus M_ninsert ignore into journalissuearticles values(I);$ and two distinct vertices $A$ and $B$ are adjacent if and only if Tr$insert ignore into journalissuearticles values(AB); \in I.$ Here Tr$insert ignore into journalissuearticles values(A);$ represents the trace of the matrix $A.$ In this paper, we exhibit some properties and structure of $\Gamma_{I^t}insert ignore into journalissuearticles values(M_ninsert ignore into journalissuearticles values(R););.$
Keywords : Trace graph, Matrix ring, Ideal based graph, clique number