About Balanced G-Designs
نویسنده
چکیده
Abstract A G-design is said to be balanced if the degree of its vertices is constant. We say that a G-design is strongly balanced, if for every i = 1, 2, ..., h, there exists a constant Ci such that dAi(x) = Ci, for every vertex x, where Ai indicates an automorphism classes (orbits) of the automorphism group of G, on its vertex-set, and dAi(x) is the number of blocks containing x as an element of Ai. We say that a G-design is simply balanced if it is balanced, but not strongly balanced. A problem is to find conditions on G for which a balanced G-design is strongly balanced. In this paper we prove that if G is regular then the correspondent Gdesign is always balanced, but not necessarily strongly balanced.
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