Listing all spanning trees in Halin graphs - sequential and Parallel view

For a connected labelled graph G, a spanning tree T is a connected and an acyclic subgraph that spans all vertices of G. In this paper, we consider a classical combinatorial problem which is to list all spanning trees of G. A Halin graph is a graph obtained from a tree with no degree two vertices and by joining all leaves with a cycle. We present a sequential and parallel algorithm to enumerate all spanning trees in Halin graphs. Our approach enumerates without repetitions and we make use of O((2pd)) processors for parallel algorithmics, where d and p are the depth, the number of leaves, respectively, of the Halin graph. We also prove that the number of spanning trees in Halin graphs is O((2pd)).