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2020 On arithmetical structures on complete graphs
Zachary Harris, Joel Louwsma
Involve 13(2): 345-355 (2020). DOI: 10.2140/involve.2020.13.345

Abstract

An arithmetical structure on the complete graph Kn with n vertices is given by a collection of n positive integers with no common factor, each of which divides their sum. We show that, for all positive integers c less than a certain bound depending on n, there is an arithmetical structure on Kn with largest value c. We also show that, if each prime factor of c is greater than (n+1)24, there is no arithmetical structure on Kn with largest value c. We apply these results to study which prime numbers can occur as the largest value of an arithmetical structure on Kn.

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Zachary Harris. Joel Louwsma. "On arithmetical structures on complete graphs." Involve 13 (2) 345 - 355, 2020. https://doi.org/10.2140/involve.2020.13.345

Information

Received: 15 September 2019; Revised: 1 January 2020; Accepted: 6 January 2020; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07184488
MathSciNet: MR4080498
Digital Object Identifier: 10.2140/involve.2020.13.345

Subjects:
Primary: 11D68
Secondary: 05C50, 11A41

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 2 • 2020
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