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FELIX LAZEBNIK, Department of Mathematical Sciences, University of
Delaware, Newark, Delaware 19716, USA |

*On a class of algebraically defined graphs* |

Let *F*^{n} denote be the *n*-dimensional vector space over a field
*F*. For and each
, let
be a function of 2*i* variables. We consider a
bipartite
graph whose vertex partitions *P* and *L* are copies of *F*^{n} with
and
being
joined by an edge if and only if the following *n*-1 equalities are
satisfied:

For particular fields *F* and particular functions *f*_{i}'s, the
families of graphs defined this way (or slightly modified) possesses
many remarkable properties. They are concerned with forbidden cycles,
girth, graph homomorphism, eigenvalues, and edge-decompositions of
complete graphs and complete bipartite graphs. In this talk we survey
some known and some new results on such graphs based on the work of
A. J. Woldar and the speaker.

** Next:** Laszlo Székely - Some
** Up:** Extremal Combinatorics / Combinatoire
** Previous:** Penny Haxell - Integer
* *