## Involve: A Journal of Mathematics

• Involve
• Volume 12, Number 4 (2019), 633-646.

### Prime labelings of infinite graphs

#### Abstract

A finite graph on $n$ vertices has a prime labeling provided there is a way to label the vertices with the integers 1 through $n$ such that every pair of adjacent vertices has relatively prime labels. We extend the definition of prime labeling to infinite graphs and give a simple necessary and sufficient condition for an infinite graph to have a prime labeling. We then measure the complexity of prime labelings of infinite graphs using techniques from computability theory to verify that our condition is as simple as possible.

#### Article information

Source
Involve, Volume 12, Number 4 (2019), 633-646.

Dates
Revised: 9 July 2018
Accepted: 8 November 2018
First available in Project Euclid: 30 May 2019

https://projecteuclid.org/euclid.involve/1559181656

Digital Object Identifier
doi:10.2140/involve.2019.12.633

Mathematical Reviews number (MathSciNet)
MR3941602

Zentralblatt MATH identifier
07072543

#### Citation

Kenigsberg, Matthew; Levin, Oscar. Prime labelings of infinite graphs. Involve 12 (2019), no. 4, 633--646. doi:10.2140/involve.2019.12.633. https://projecteuclid.org/euclid.involve/1559181656

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