What question did this study set out to answer?

The study aims to investigate the isomorphism problem and the perfectness of zero-divisor graphs associated with finite MV-algebras.

April 30, 2026

Isomorphism problem and perfectness of zero-divisor graphs for finite MV-algebras

Key Points

The study aims to investigate the isomorphism problem and the perfectness of zero-divisor graphs associated with finite MV-algebras.
Analyzed the structure of the zero-divisor graph formed by finite MV-algebras.
Examined invariants such as domination parameters, chromatic number, and clique number.
Proved that B3(A) B3(B) implies A B3 B if A and B are finite MV-algebras with |A|=|B| B5 5.
Demonstrated that the chromatic number equals the clique number for the zero-divisor graph of a finite MV-algebra.
Established that isomorphic zero-divisor graphs indicate isomorphic finite MV-algebras for sufficiently large algebras.
Characterized the conditions under which the zero-divisor graph is perfect.

Abstract

Abstract Let (A;, , 0) be a finite MV-algebra, and (A;, 0) be the associated semigroup. The zero-divisor graph (A) of A is a simple graph with the set of vertices align* &V ( (A) ) =\x A \{0\ (~y A\0\) ~x~~y=0\}, align* and the set of edges E ( (A) ) =the edge with ends x and y (x, y A \{0\, x y) ~x~ ~y=0}. In this paper, some invariants (such as domination parameters, isomorphism problems, the chromatic number and the clique number, perfectness, etc. ) of (A) are discussed. We prove that (A) (B) implies that A B when A and B are finite MV-algebras with |A|=|B| 5. Also, for a finite MV-algebra A, we obtain that the chromatic number of (A) equals the clique number of (A), and characterize the perfectness of (A).

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