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Eigenvalue of Adjacent Matrix of Zero Divisor Graphs on Rings

Journal: Engineering and Technology Quarterly Reviews (Vol.3, No. 2)

Publication Date:

Authors : ;

Page : 63-66

Keywords : Eigenvalue; Adjacency Matrix; Zero Devisors Graph of Commutative Ring;

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Abstract

Let R be a commutative ring with identity 1≠0 and T be the ring of all nxn upper triangular matrices over R. The zero-devisor graph of T denoted by T(Tn(R)). In this paper, I define the adjacent Matrix of T(R) and T(Tn(R)). Then I describe the relation between the non-zero Eigenvalues of adjacent Matrix of these graph and edges. After I use these result to determination of Eigenvalue adjacent matrix of T(T2(R)).

Last modified: 2020-09-02 22:24:48