Name
Abstract | ||
|---|---|---|
Let e be a positive integer, p be an odd prime, q=p^e, and F"q be the finite field of q elements. Let f"2,f"3@?F"q[x,y]. The graph G=G"q(f"2,f"3) is a bipartite graph with vertex partitions P=F"q^3 and L=F"q^3, and edges defined as follows: a vertex (p)=(p"1,p"2,p"3)@?P is adjacent to a vertex [l]=[l"1,l"2,l"3] if and only ifp"2+l"2=f"2(p"1,l"1)andp"3+l"3=f"3(p"1,l"1). Motivated by some questions in finite geometry and extremal graph theory, we ask when G has no cycle of length less than eight, i.e., has girth at least eight. When f"2 and f"3 are monomials, we call G a monomial graph. We show that for p=5, and e=2^a3^b, a monomial graph of girth at least eight has to be isomorphic to the graph G"q(xy,xy^2), which is an induced subgraph of the classical generalized quadrangle W(q). For all other e, we show that a monomial graph is isomorphic to a graph G"q(xy,x^ky^2^k), with 1= |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.ffa.2006.03.001 | Finite Fields and Their Applications |
Keywords | Field | DocType |
vertex partitions p,induced subgraph,finite field,bipartite graph,q element,extremal graph theory,finite geometry,graph g,classical generalized quadrangle,monomial graph,cycle,satisfiability | Discrete mathematics,Combinatorics,Circulant graph,Edge-transitive graph,Graph power,Algebra,Cycle graph,Foster graph,Function composition,Symmetric graph,Extremal graph theory,Mathematics | Journal |
Volume | Issue | ISSN |
13 | 4 | 1071-5797 |
Citations | PageRank | References |
11 | 1.46 | 9 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Vasyl Dmytrenko | 1 | 14 | 1.99 |
| Felix Lazebnik | 2 | 353 | 49.26 |
| Jason Williford | 3 | 38 | 4.54 |