| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4647898 | Discrete Mathematics | 2012 | 8 Pages |
Abstract
A graph GG has a representation modulo rr if there exists an injective map f:V(G)→{0,1,…,r−1}f:V(G)→{0,1,…,r−1} such that vertices uu and vv are adjacent if and only if f(u)−f(v)f(u)−f(v) is relatively prime to rr. The representation number rep(G) is the smallest rr such that GG has a representation modulo rr. Following earlier work on stars, we study representation numbers of complete bipartite graphs and more generally complete multipartite graphs.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Reza Akhtar, Anthony B. Evans, Dan Pritikin,