Generating all degree constrained and degree preserving spanning trees of a weighted graph in order of increasing cost

The degree constrained minimum spanning tree problem is to determine a spanning tree of the minimum total edge cost and degree no more than a given value d (d-MST). A number of algorithms have been proposed for this problem. In [1] we introduced a new spanning tree called vertex subset degree preserving spanning tree, which was defined as a spanning tree T such that , v A-a non empty subset of the vertex set V of the graph G. This paper presents two algorithms to generate all degree constrained spanning trees and all vertex subset degree preserving spanning trees of a weighted graph in order of increasing cost. By generating spanning trees in order of increasing cost, it is possible to determine the second smallest or in general the k-th smallest spanning tree of a graph. Time complexity analyses are also given.