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A tree with at most k leaves is called k-ended tree, and a tree with exactlyk 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 andidentifying its end vertices and deleting all edges between every two vertexexcept one edge to gain again a simple graph and is denoted bye G/e. In thispaper we prove some theorems related to a graph and its contraction. Forexample we prove the following theorem. If G is a connected graph that has aspanning k-end tree and |V (G)| > K + 1 then there exist an edge e such G/e hasa spanning k-end tree.

Contraction of graphs and spanning k-end trees