Engineering and Technology Quarterly Reviews

ISSN 2622-9374

Published: 03 September 2020

Eigenvalue of Adjacent Matrix of Zero Divisor Graphs on Rings

Hemati Sherin

Bamyan University, Afghanistan

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10.5281/zenodo.4011991

Pages: 63-66

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

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)).

References

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