Digraphs with at most one trivial critical ideal

2017/09/28 by Carlos A. Alfaro, Carlos E. Valencia, Adrián Vázquez-Ávila · 1 citation
Mathematics · Computer Science · #Graph theory and applications #Topological and Geometric Data Analysis #Commutative Algebra and Its Applications

paper · doi:10.1080/03081087.2017.1383349

Abstract

Critical ideals generalize the critical group, Smith group and the characteristic polynomials of the adjacency and Laplacian matrices of a graph. We give a complete characterization of the digraphs with at most one trivial critical ideal. Which implies the characterizations of the digraphs whose critical group has one invariant factor equal to one, and the digraphs whose Smith group has one invariant factor equal to one.

Cited by

• Eigenvalues, Smith normal form and determinantal ideals

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