Signed Zero-Divisor Graphs Over Commutative Rings

Abstract

In this paper, we define signed zero-divisor graphs over commutative rings and investigate the interplay between the algebraic properties of the rings and the combinatorial properties of their corresponding signed zero-divisor graphs. We investigate the structure of signed zero-divisor graphs, the relation between ideals and signed zero-divisor graphs, and the adjacency matrices and the spectra of signed zero-divisor graphs.

Keywords

Ring / Ideal / Signed graph / Adjacency matrix

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