Prime labelings on a 3xn grid graph
Affiliation of Author, Researcher, or Creator
Marlboro Institute of Liberal Arts and Interdisciplinary Studies
Department
Marlboro Institute for Liberal Arts and Interdisciplinary Studies
Author(s)
S. J. Curran and M. A. Ollis
Resource Type
Article
Publication, Publisher or Distributor
Theory and Applications of Graphs
Publication Date
2025
Brief Description
A graph is a network of nodes, connected by edges. A graph with n nodes is prime if it is possible to label the nodes with the integers 1, 2, ... n in such a way that any two nodes that are connected by an edge have coprime labels. It is conjectured that all grid graphs---networks with nodes laid out in a rectangular grid and edges between orthogonally adjacent ones---have a prime labeling. In this paper it is shown that if the number theoretic conjectures Goldbach's Even Conjecture and a strengthened version of Lemoine's Conjecture hold then every 3 x n grid graph is prime.
Keywords
math, graph, prime, labeling
Recommended Citation
Curran, S. J. and Ollis, M. A. (2025) "Prime labelings on a 3xn grid graph," Theory and Applications of Graphs: Vol. 12: Iss. 1, Article 4. DOI: 10.20429/tag.2025.120104
Preferred Citation Style
Other
Peer Reviewed
1
Creative Commons License
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