A geometric spanning tree of a point set S is a tree whose vertex set is S and whose edge set is a set of non-crossing straight line segments with endpoints in S. Given a set of red points and a set of blue points in the plane, the red/blue spanning tree problem is to find a geometric spanning tree for red points and a geometric spanning tree for blue points such that the number of crossing poi...

The most popular algorithms for generation of minimal spanning tree are Kruskal’s[2] and Prim’s[2] algorithm. Many algorithms have been proposed for generation of all spanning tree. This paper deals with generation of all possible spanning trees in increasing cost of a weighted graph. This approach uses one matrix called Difference Weighted Circuit Matrix (DWCM); it is little bit modification o...

In 2006, Suzuki, and Akbari & Alipour independently presented a necessary and sufficient condition for edge-colored graphs to have a heterochromatic spanning tree, where a heterochromatic spanning tree is a spanning tree whose edges have distinct colors. In this paper, we propose f -chromatic graphs as a generalization of heterochromatic graphs. An edge-colored graph is f -chromatic if each col...

This paper combines social choice theory with discrete optimization. We assume that individuals have preferences over edges of a graph that need to be aggregated. The goal is to nd a socially best spanning tree in the graph. As ranking all spanning trees is becoming infeasible even for small numbers of vertices and/or edges of a graph, our interest lies in nding algorithms that determine a soci...

Spanning Tree Protocol (STP) is a link management protocol that provides path redundancy while preventing undesirable loops in the Ethernet networks. In fact, STP defines a tree that spans all switches in the network such that the sum of the costs of the chosen links is minimized. Deploying the STP to manage the topology autonomously is inadequate and do not meet the requirement for Metro Area ...

We are given a set P of points in the plane, together with a partition of P into classes of points; i.e., each point of P belongs to exactly one class. For a given network optimization problem, such as nding a minimum spanning tree or nding a minimum diameter spanning tree, we study the problem of choosing a subset P 0 of P that contains at least one point of each class and solving the network ...

Previous studies has shown that for a weighted undirected graph having n vertices and m edges, a minimal weight spanning tree can be found with O (√ mn ) calls to the weight oracle. The present note shows that a given spanning tree can be verified to be a minimal weight spanning tree with only O (

In this paper we consider the spanning tree congestion for several families of graphs. We find the exact spanning tree congestion for toroidal meshes, Cm×Cn, and cylindrical meshes, Pm×Cn,. Also we find bounds for the spanning tree congestion of Qn, and a construction that gives the upper bound.