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A graph \( G \) is said to be a \( (2, k) \)-regular graph if each vertex of \( G \) is at a distance two away from \( k \) vertices of \( G \). A graph \( G \) is called an \( (r, 2, k) \)-regular graph if each vertex of \( G \) is at a distance \( 1 \) away from \( r \) vertices of \( G \) and each vertex of \( G \) is at a distance \( 2 \) away from \( k \) vertices of \( G \) \cite{9}. This paper suggests a method to construct a \( ((m + n – 2), 2, (m – 1)(n – 1)) \)-regular graph of smallest order \( mn \) containing a given graph \( G \) of order \( n \geq 2 \) as an induced subgraph for any \( m > 1 \).