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We proved that if a complete bipartite framework K (m, n) (m \u003e= 3, n \u003e= 5) in the plane admits a continuous deformation, then one of the partite-sets lies on a line L and the other partite-set lies on the line perpendicular to L.\\n2.On embeddings of structures : We proved that for any planar graph G = (V,E), there is an emebedding f : V * R^2 such that x, y * V are adijacent if and only if the distance between f (x) and f (y) is an integer. We also proved that every n dimensional inner product space over the rational field can be isometrically embedded into 2n + 1 dimensional Euclidean space.\\n3.On srrangements of spheres : A graph G is said to be representable by balls on the table, if we can place solid balls on a table, one ball for each vertex, so that two balls are tangent only when the corresponding vertices are adjacent. 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