  We propose a new model for graph editing problems on intersection graphs. In
well-studied graph editing problems, adding and deleting vertices and edges are
used as graph editing operations. As a graph editing operation on intersection
graphs, we propose moving objects corresponding to vertices. In this paper, we
focus on interval graphs as an intersection graph. We give a linear-time
algorithm to find the total moving distance for transforming an interval graph
into a complete graph. The concept of this algorithm can be applied for (i)
transforming a unit square graph into a complete graph over $L_1$ distance and
(ii) attaining the existence of a $k$-clique on unit interval graphs. In
addition, we provide LP-formulations to achieve several properties in the
associated graph of unit intervals.
