The minimum spanning tree (MST) is widely used in planning the most economical network. algorithm for finding MST of a connected graph essential. In this paper, new proposed based on deduced theorem MST. first sorts edges according to their weight, from large small. Next, premise ensuring connectivity graph, it deletes order until number equal vertexes minus 1. Finally, remaining an This equiva...

Given a graph G with a speciied root node r. A spanning tree in G where each node has distance at most 2 from r is called a 2-hop spanning tree. For given edge weights the 2-hop spanning tree problem is to nd a minimum weight 2-hop spanning tree. The problem is NP-hard and has some interesting applications. We study a polytope associated with a directed model of the problem give a completeness ...

The concept of the minimum spanning tree (MST) plays an important role in topological network design, because it models a cheapest connected network. In a tree, however, the failure of a vertex can disconnect the network. In order to tolerate such a failure, we generalize the MST to the concept of a cheapest biconnected network. For a set of points in the Euclidean plane, we show that it is NP-...