Conditions for Digraphs Representation of the Characteristic Polynomial

Abstract

This paper presents additional conditions that are needed to create proper digraphs representation of the characteristic polynomial. Contrary to currently used methods (like canonical forms) digraphs representations allow to find a complete set of all possible realisations instead of only a few realisations. In addition, all realisations in the set are minimal. Proposed additional conditions on creating digraphs representations allow faster creation of representations by restricting the creations of representations that are not proper and would have to be removed in later steps of algorithm.