Distance ideals of digraphs

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-03-28 DOI:10.1016/j.amc.2025.129430

Carlos A. Alfaro , Teresa I. Hoekstra-Mendoza , Juan Pablo Serrano , Ralihe R. Villagrán

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引用次数: 0

Abstract

We focus on strongly connected, strong for short, digraphs since in this setting distance is defined for every pair of vertices. Distance ideals generalize the spectrum and Smith normal form of several distance matrices associated with strong digraphs. We introduce the concept of pattern which allow us to characterize the family

Γ_{1}

of digraphs with only one trivial distance ideal over

Z

. This result generalizes an analogous result for undirected graphs that states that connected graphs with one trivial ideal over

Z

consists of either complete graphs or complete bipartite graphs. It turns out that the strong digraphs in

Γ_{1}

consists in the circuit with 3 vertices and a family Λ of strong digraphs that contains complete graphs and complete bipartite graphs, regarded as digraphs. We also compute all distance ideals of some strong digraphs in the family Λ. Then, we explore the distance ideals of circuits, which turns out to be an infinite family of digraphs with unbounded diameter in

Γ_{2}

, that is, digraphs with two trivial distance ideals.

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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.