A New Type of Zero Divisor Graphs of a Lattice, t-Zero Divisor Graphs

Year 2025, Volume: 17 Issue: 2, 562 - 572, 30.12.2025

Dilek Bayrak Delice

https://doi.org/10.47000/tjmcs.1767545

Abstract

In this paper, we introduce the t-zero divisor graph $\Gamma_{T}(L)$, which is a generalization of the zero divisor graph of a lattice $\Gamma(L)$, where $t$ is a triangular norm on $L$. We investigate which properties hold in $t$-zero divisor graphs for special $t$-norms while giving some additional properties of the zero divisor graph. Additionally, the cases where the zero divisor graph and the t-zero divisor graph are line graphs are investigated.

Keywords

zero-divisor graph , t-norm , lattice.

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