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We describe the Betti numbers of the edge ideals $I(G)$ of uniformhypergraphs $G$ such that $I(G)$ has linear graded free resolution. We give analgebraic equation system and some inequalities for the components of the$f$--vector of the clique complex of an arbitrary chordal graph. Finally wepresent an explicit formula for the multiplicity of the Stanley-Reisner ring ofthe edge ideals of any chordal graph.

The $f$--vector of the clique complex of chordal graphs and Betti numbers of edge ideals of uniform hypergraphs