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## Ideal based trace graph of matrices

#### Tamizh Chelvam THİRUGNANAM [1] , M. SİVAGAMİ [2]

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 $\Gamma_{I^t}(M_n(R)).$
Trace graph, Matrix ring, Ideal based graph, clique number
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Birincil Dil en Matematik Matematik Orcid: 0000-0002-1878-7847Yazar: Tamizh Chelvam THİRUGNANAM (Sorumlu Yazar)Kurum: Manonmaniam Sundaranar UniversityÜlke: India Orcid: 0000-0002-9624-7627Yazar: M. SİVAGAMİ Kurum: Manonmaniam Sundaranar UniversityÜlke: India Yayımlanma Tarihi : 2 Nisan 2020
 Bibtex @araştırma makalesi { hujms478373, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2020}, volume = {49}, pages = {608 - 616}, doi = {10.15672/hujms.478373}, title = {Ideal based trace graph of matrices}, key = {cite}, author = {THİRUGNANAM, Tamizh Chelvam and SİVAGAMİ, M.} } APA THİRUGNANAM, T , SİVAGAMİ, M . (2020). Ideal based trace graph of matrices. Hacettepe Journal of Mathematics and Statistics , 49 (2) , 608-616 . DOI: 10.15672/hujms.478373 MLA THİRUGNANAM, T , SİVAGAMİ, M . "Ideal based trace graph of matrices". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 608-616 Chicago THİRUGNANAM, T , SİVAGAMİ, M . "Ideal based trace graph of matrices". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 608-616 RIS TY - JOUR T1 - Ideal based trace graph of matrices AU - Tamizh Chelvam THİRUGNANAM , M. SİVAGAMİ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.478373 DO - 10.15672/hujms.478373 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 608 EP - 616 VL - 49 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.478373 UR - https://doi.org/10.15672/hujms.478373 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Ideal based trace graph of matrices %A Tamizh Chelvam THİRUGNANAM , M. SİVAGAMİ %T Ideal based trace graph of matrices %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 2 %R doi: 10.15672/hujms.478373 %U 10.15672/hujms.478373 ISNAD THİRUGNANAM, Tamizh Chelvam , SİVAGAMİ, M. . "Ideal based trace graph of matrices". Hacettepe Journal of Mathematics and Statistics 49 / 2 (Nisan 2020): 608-616 . https://doi.org/10.15672/hujms.478373 AMA THİRUGNANAM T , SİVAGAMİ M . Ideal based trace graph of matrices. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 608-616. Vancouver THİRUGNANAM T , SİVAGAMİ M . Ideal based trace graph of matrices. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 616-608.

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