Abstract: In this paper an inverse problem is intrnduced, which determined the shape of the unknown region D in R³ nonhomogenous geoelectrical domain Ω with point sources. The existence of such problem is proved by sobolev theory. A new approach is given, which is based on a variational princible combined with an application of graphic theory. According this method, the numerical results are given. They show that this approach is feasible and effective. It can be also applied to solve other kind of inverse problem.

Key words: nverse problem, sobolev space, trace theorem, broad first search method, deep first search method