Characterizatio n of the n-th Super-eulerian Iterated Line Graph

A branch of a graph is a nontrivial path whose ends ha ve not degree 2 and whose internal vertices,if any,have degree 2.In this pa per,it is showed that the n-th iterated line graphL-n(G ) of a connected graph G is super-eulerian graph if and only if G contains a subgraph H which contains all the vertic es of degree at least 3,each of vertices of H have even degree in H,any isolated vertex of H has degree of at least 3 in G,the distance between any component of H and the ot hers in H is at most n,any branch of G which is not belong to H has length at most n+1,the legt h of any branch which has end of degree one is at most n.