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An undirected graph possesses an eulerian circuit if and only if it is connected and its vertices are  All of even degree .

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makhdoom ghaya asked Sep 5, 2016
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The minimum number of edges in a connected graph with $‘n’$ vertices is equal to$n (n – 1)$ $\frac{n(n-1)}{2}$$n^{2}$$n – 1$