In this paper we learn the new idea of forcing total outer independent edge geodetic number a graph. Let G be connected graph and R minimum set G. A subset L ⊆ is known as for if unique containing L. cardinality R. The denoted by (G) = min , where taken over all in Some general properties satisfied concept are studied. It shown that any couple integers l, m with0 < l ≤ − 4, there exists such .