Graph algebras

2019/12/11 by Piotr M. Hajac, Hajac, Piotr M., Mariusz Tobolski +1 · 5 citations
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1912.05136

openalex publication_date 2019/12/11 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

This introduction to graphs and graph algebras provides the optimal bound for the number of all paths of length k in a graph with N≥ k edges and no loops. Our proof relies on a construction of a number of terminating algorithms that reshape such graphs without ever decreasing the number of paths of length k. The key two algorithms work in turns each of them ending with a graph to which the other algorithm can be applied. Finally, one arrives at a specific graph realizing the optimal bound. Herein graph algebras mean path algebras and Leavitt path algebras. For the ground field ℂ of complex numbers, the latter are viewed as dense subalgebras in their universal C*-completions called graph C*-algebras.

Cited by

• A topological approach to discrete restriction semigroups and their algebras
• On amplified graph C*-algebras as cores of Cuntz-Krieger algebras
• Maximal 2-extensions of Pythagorean fields and Right Angled Artin Groups
• Minimality and effectiveness of the groupoid associated to a self-similar ultragraph
• Relating insplittings of 2-graphs and of textile systems

Related

• Counting paths in directed graphs
• Finding A Path Of Length k: An Expository
• Purely infinite simple Leavitt path algebras
• An Algebraic Approach to the Longest Path Problem
• Leavitt path algebras and direct limits