Translator Disclaimer
2019 Prime labelings of infinite graphs
Matthew Kenigsberg, Oscar Levin
Involve 12(4): 633-646 (2019). DOI: 10.2140/involve.2019.12.633

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.

Citation

Download Citation

Matthew Kenigsberg. Oscar Levin. "Prime labelings of infinite graphs." Involve 12 (4) 633 - 646, 2019. https://doi.org/10.2140/involve.2019.12.633

Information

Received: 22 February 2018; Revised: 9 July 2018; Accepted: 8 November 2018; Published: 2019
First available in Project Euclid: 30 May 2019

zbMATH: 07072543
MathSciNet: MR3941602
Digital Object Identifier: 10.2140/involve.2019.12.633

Subjects:
Primary: 03D80, 05C63, 05C78, 05C85

Rights: Copyright © 2019 Mathematical Sciences Publishers

JOURNAL ARTICLE
14 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.12 • No. 4 • 2019
MSP
Back to Top