A combinatorial algorithm to generate all spanning trees of a weighted graph in order of increasing cost

TL;DR

This paper introduces a new combinatorial algorithm that efficiently generates all spanning trees of a weighted graph in order of increasing cost, using a modified matrix approach.

Contribution

It proposes a novel algorithm based on the Difference Weighted Circuit Matrix for systematic generation of all spanning trees by increasing cost.

Findings

Efficient generation of all spanning trees in increasing order of cost.

Utilizes a modified FCM called Difference Weighted Circuit Matrix.

Provides a new approach for spanning tree enumeration in weighted graphs.

Abstract

The most popular algorithms for generation of minimal spanning tree are Kruskal and Prim 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; it is little bit modification of FCM.