# Finding All Breadth First Full Spanning Trees in a Directed Graph

Hoda Khalil and Yvan Labiche

July 2017

### Abstract

This paper proposes an algorithm that is particularly concerned with generating all possible distinct spanning trees that are based on breadth-first-search directed graph traversal. The generated trees span all edges and vertices of the original directed graph. The algorithm starts by generating an initial tree, and then generates the rest of the trees using elementary transformations. It runs in O(E+T) time where E is the number of edges and T is the number of generated trees. In the worst-case scenario, this is equivalent to O (E+En/Nn) time complexity where N is the number of nodes in the original graph. The algorithm requires O(T) space. However, possible modifications to improve the algorithm space complexity are suggested. Furthermore, experiments are conducted to evaluate the algorithm performance and the results are listed.

Publication

2017 IEEE 41st Annual Computer Software and Applications Conference