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We give a sharp bound on the number of triangles in a graph with fixed number of edges. We also characterize graphs that achieve the maximum number of triangles. Using the upper bound on number of triangles, we give a sharp bound for the size of the Schur multiplier of special  p -group of all ranks. We also improve existing bounds for the size of Schur multiplier of  p -groupsof class, and for  p -groups of coclass  r .

The maximum number of triangles in a graph and its relation to the size of the Schur multiplier of special p -groups