Vol. 10, No. 1, 2017

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Prime labelings of generalized Petersen graphs

Steven A. Schluchter, Justin Z. Schroeder, Kathryn Cokus, Ryan Ellingson, Hayley Harris, Ethan Rarity and Thomas Wilson

Vol. 10 (2017), No. 1, 109–124
Abstract

A graph G is called prime if the vertices of G can be assigned distinct labels 1,2,,|V (G)| such that the labels on any two adjacent vertices are relatively prime. By showing that for every even n 2.468 × 109 there exists s [1,n 1] such that both n + s and 2n + s are prime, we prove the generalized Peterson graph P(n,1) is prime for all even n [4,2.468 × 109]. Moreover, for a fixed n we describe a method for labeling P(n,k) that is a prime labeling for multiple values of k. Using this method, we prove P(n,k) is prime for all even n 50 and all odd k [1,n2).

Keywords
graph labeling, generalized Petersen graph, prime graph
Mathematical Subject Classification 2010
Primary: 05C78
Milestones
Received: 8 September 2015
Revised: 20 November 2015
Accepted: 28 November 2015
Published: 11 October 2016

Communicated by Joseph A. Gallian
Authors
Steven A. Schluchter
Department of Mathematical Sciences
George Mason University
4400 University Drive
MS: 3F2
Fairfax, VA 22030
United States
Justin Z. Schroeder
Mosaic Centre Radstock
Kej Bratstvo Edinstvo 45
1230 Gostivar
Macedonia
Kathryn Cokus
George Mason University
4400 University Drive
Fairfax, VA 22030
United States
Ryan Ellingson
George Mason University
4400 University Drive
Fairfax, VA 22030
United States
Hayley Harris
George Mason University
4400 University Drive
Fairfax, VA 22030
United States
Ethan Rarity
George Mason University
4400 University Drive
Fairfax, VA 22030
United States
Thomas Wilson
George Mason University
4400 University Drive
Fairfax, VA 22030
United States