Comments on "On multi-consensus and almost equitable graph partitions"

Abstract

The main theorem of the quoted paper (Theorem 1) claims that the coarsest almost equitable partition (AEP) and clusters of multi-consensus are necessary and sufficient condition for each other. Unfortunately, the sufficiency is not. This correspondence provides a counterexample to that theorem and points out a logical flaw in its proof. (c) 2024 Elsevier Ltd.