  A tree with at most k leaves is called k-ended tree, and a tree with exactly
k leaves is called k-end tree, where a leaf is a vertex of degree one.
Contraction of a graph G along the edge e means deleting the edge e and
identifying its end vertices and deleting all edges between every two vertex
except one edge to gain again a simple graph and is denoted bye G/e. In this
paper we prove some theorems related to a graph and its contraction. For
example we prove the following theorem. If G is a connected graph that has a
spanning k-end tree and |V (G)| > K + 1 then there exist an edge e such G/e has
a spanning k-end tree.
