On The Closure Of A Graph With Cut Vertices

Let \(K\) be a maximal block of a graph \(G\) and let \(x\) and \(y\) be two nonadjacent vertices of \(G\). If \(|V(X)| \leq \frac{1}{2}(n+3)\) and \(x\) and \(y\) are not cut vertices, we show that \(x\) is not adjacent to \(y\) in the closure \(c(G)\) of \(G\). We also show that, if \(x, y \notin V(K)\), then \(x\) is not adjacent to \(y\) in \(c(G)\).