This paper investigates the minimum spanning tree problem in the framework of uncertainty theory, where the edge weights are assumed as uncertain variables. The concept of ideal uncertain minimum spanning tree is initiated by extending the definition of the uncertain α-minimum spanning tree. On the basis of this new concept, we propose the definition of uncertain distribution-minimum spanning t...

An inverse minimum spanning tree problem is to make the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. In this paper, the stochastic inverse minimum spanning tree problem is investigated. The concept of α-minimum spanning tree is initiated, and subsequently an α-minimum spanning tree model and a pro...

In this article, we provide a constructive procedure to generate a spanning tree for any graph from its dominating set, γ set. We introduce a new kind of minimum dominating set and hence generate a minimum weighted spanning tree from a γ set for G. We also provide a method for generating a minimum weighted spanning tree using adjacency matrix of G. Key–Words: Spanning tree, Minimum dominating s...

The quadratic minimum spanning tree problem is to find a spanning tree on a graph that minimizes a quadratic objective function of the edge weights. In this paper, the quadratic minimum spanning tree problem is concerned on the graph with edge weights being assumed as uncertain variables. The notion of the uncertain quadratic -minimum spanning tree is introduced by using the uncertain chance co...