In this paper we consider the Degree Constrained Minimum Spanning Tree Problem. This
problem is concerned with finding, in a given edge weighted graph G (all weights are non-negative),
the minimum weight spanning tree T satisfying specified degree restrictions on the
vertices. This problem arises naturally in communication networks where the degree of a vertex
represents the number of line interfaces available at a center. Because of its NP-completeness, a
number of heuristics have been proposed. In this paper we propose two new search methods: one
based on the method of Tabu search and the other based on a penalty function approach. For
comparative analysis, we test our methods on some benchmark problems. The computational
results support our methods.