Name
Abstract | ||
|---|---|---|
Let F be a field. For a polynomial f ¿ F x , y , we define a bipartite graph ¿ F ( f ) with vertex partition P ¿ L , P = F 3 = L , and ( p 1 , p 2 , p 3 ) ¿ P is adjacent to l 1 , l 2 , l 3 ¿ L if and only if p 2 + l 2 = p 1 l 1 and p 3 + l 3 = f ( p 1 , l 1 ) . It is known that the graph ¿ F ( x y 2 ) has no cycles of length less than eight. The main result of this paper is that ¿ F ( x y 2 ) is the only graph ¿ F ( f ) with this property when F is an algebraically closed field of characteristic zero; i.e.¿over such a field F , every graph ¿ F ( f ) with no cycles of length less than eight is isomorphic to ¿ F ( x y 2 ) . We also prove related uniqueness results for some polynomials f over infinite families of finite fields. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.dam.2016.01.017 | Discrete Applied Mathematics |
Keywords | Field | DocType |
Algebraically defined graph,Cycle,Girth eight,Lefschetz principle,Finite field,Generalized quadrangle | Discrete mathematics,Graph,Uniqueness,Combinatorics,Finite field,Polynomial,Bipartite graph,Isomorphism,Generalized quadrangle,Mathematics,Algebraically closed field | Journal |
Volume | Issue | ISSN |
206 | C | 0166-218X |
Citations | PageRank | References |
2 | 0.47 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Brian G. Kronenthal | 1 | 8 | 1.87 |
| Felix Lazebnik | 2 | 353 | 49.26 |