Name
Abstract | ||
|---|---|---|
A graph G is a prime distance graph (respectively, a 2-odd graph) if its vertices can be labeled with distinct integers such that for any two adjacent vertices, the difference of their labels is prime (either 2 or odd). We prove that trees, cycles, and bipartite graphs are prime distance graphs, and that Dutch windmill graphs and paper mill graphs are prime distance graphs if and only if the Twin Prime Conjecture and de Polignac’s Conjecture are true, respectively. We give a characterization of 2-odd graphs in terms of edge colorings, and we use this characterization to determine which circulant graphs of the form Circ(n,{1,k}) are 2-odd and to prove results on circulant prime distance graphs. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.disc.2013.06.005 | Discrete Mathematics |
Keywords | Field | DocType |
Distance graphs,Prime distance graphs,Difference graphs | Discrete mathematics,Odd graph,Combinatorics,Indifference graph,Chordal graph,Clique-sum,Graph product,Cograph,Pathwidth,1-planar graph,Mathematics | Journal |
Volume | Issue | ISSN |
313 | 20 | 0012-365X |
Citations | PageRank | References |
0 | 0.34 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Joshua D. Laison | 1 | 38 | 7.08 |
| Colin Starr | 2 | 0 | 0.68 |
| Andrea Walker | 3 | 0 | 0.34 |