Cycles, wheels, and gears in finite planes


  • Jamie Peabody
  • Oscar Vega California State University, Fresno
  • Jordan White



Graph embeddings, finite projective plane, primitive element


The existence of a primitive element of $GF(q)$ with certain properties is used to prove that all cycles that could theoretically be embedded in $AG(2,q)$ and $PG(2,q)$ can, in fact, be embedded there (i.e. these planes are `pancyclic'). We also study embeddings of wheel and gear graphs in arbitrary projective planes.

Author Biography

Oscar Vega, California State University, Fresno

Assistant Professor

Department of Mathematics


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