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A graph inequality on the common neighbourhood (1912.00417v1)
Published 1 Dec 2019 in math.CO
Abstract: In this note we prove a graph inequality based on the sizes of the common neighbourhoods. We also characterize the extremal graphs that achieve the equality. The result was first discovered as a consequence of the classical Forster's theorem in electric networks. We also present a short combinatorial proof that was inspired by a similar inequality related to the celebrated Tur\'an's theorem.