Abstract
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-groups of class , and for p-groups of coclass r.
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