Given an undirected graphG $=($V$,$ E$),$ the transformed graphGI $=($V$,$ ET$)$ is defined such thatuv E El if and only if uv E E or there is a vertex W$,$ W FU$,$ W FU$,$ such that uw E E and wu e E$.$Design efficient algorithms for computing GI from G for both the adjacency$-$list and the adjacency$-$matrix representations.