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Graphs and Combinatorics

, Volume 35, Issue 1, pp 119–140 | Cite as

Every Cubic Bipartite Graph has a Prime Labeling Except \(K_{3,3}\)

  • J. Z. SchroederEmail author
Original Paper
  • 55 Downloads

Abstract

A graph G is prime if the vertices can be distinctly labeled with the integers \(1,2, \ldots ,|V(G)|\) so that adjacent vertices have relatively prime labels. We show that every cubic bipartite graph is prime except \(K_{3,3}\), which implies a number of other results. We also provide evidence to support a conjectured classification for the primality of 2-regular graphs.

Keywords

Prime labeling Bipartite graph Regular graph 

Mathematics Subject Classification

05C78 

Supplementary material

373_2018_1980_MOESM1_ESM.pdf (81 kb)
Supplementary material 1 (pdf 81 KB)

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Copyright information

© Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mosaic Center RadstockGostivarMacedonia

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