Name
Abstract | ||
|---|---|---|
Let F be a field. For a polynomial f∈F[x,y]
and positive integers k and m, we define a bipartite graph ΓF(xkym,f) with vertex partition P∪L, where P and L are two copies of F3, and (p1,p2,p3)∈P is adjacent to [l1,l2,l3]∈L if and only if p2+l2=p1kl1mandp3+l3=f(p1,l1)It is known that ΓF(xy,xy2) has no cycles of length less than eight. The main result of this paper is that ΓF(xy,xy2) is the only graph ΓF(xkym,f) with this property when F is an algebraically closed field of characteristic zero; i.e. over such a field F, every graph ΓF(xkym,f) with no cycles of length less than eight is isomorphic to ΓF(xy,xy2). We also prove related uniqueness results over infinite families of finite fields. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.dam.2018.06.020 | Discrete Applied Mathematics |
Keywords | Field | DocType |
Algebraically defined graph,Cycle,Girth eight,Lefschetz principle,Finite field,Generalized quadrangle | Integer,Discrete mathematics,Uniqueness,Graph,Combinatorics,Finite field,Polynomial,Bipartite graph,Isomorphism,Algebraically closed field,Mathematics | Journal |
Volume | ISSN | Citations |
254 | 0166-218X | 1 |
PageRank | References | Authors |
0.39 | 4 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Brian G. Kronenthal | 1 | 8 | 1.87 |
| Felix Lazebnik | 2 | 353 | 49.26 |
| Jason S. Williford | 3 | 12 | 3.39 |