2022/08/17 by Holly Carter, Carter, Holly, N. Bradley Fox +1
Computer Science · #05C78 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2208.08488
openalex publication_date 2022/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An odd prime labeling is a variation of a prime labeling in which the vertices of a graph of order~n are labeled with the distinct odd integers 1 to 2n-1 so that the labels of adjacent vertices are relatively prime. This paper investigates many different classes of graphs including disjoint unions of cycles, stacked prisms, and particular types of caterpillars, by using various methods to construct odd prime labelings. We also demonstrate progress toward proving a conjecture that all prime graphs have an odd prime labeling.