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arXiv · 1511.01696

Listing All Spanning Trees in Halin Graphs - Sequential and Parallel view

K. Krishna Mohan Reddy·P. Renjith·N. Sadagopan
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Abstract

For a connected labelled graph $G$, a {\em 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 $O((2pd)^{p})$ 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 $O((2pd)^{p})$.

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K. Krishna Mohan Reddy, P. Renjith, N. Sadagopan. 2016-07-20. Listing All Spanning Trees in Halin Graphs - Sequential and Parallel view. https://arxiv.org/abs/1511.01696

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