Abstract algebra

Abstract algebra
1-letG=(V,E)be a finite graph and let v?V be a vertex. We set Gv = {w ? V | {v, w} ? E}, and call Gv the star of v, or the vertex neighborhood of v. or if for all v?V,we have|Gv|=k for some fixed integer k,we call Ga k-valent graph. now prove this. Assume that G = Aut G acts transitively on the vertices of G. Prove that G is k-valent, for some k. (note that the converse is false!)

hint: Let v,w ? V

NTS: valence of v= valence of w

or #of edges of v= # of edges of w

or |{edges of v}|=|{edges of w|

prove that is (1-1). try to use one to one to prove that

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