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

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...

Listing all the minimum spanning trees in an undirected graph

Efficient polynomial time algorithms are well known for the minimum spanning tree problem. However, given an undirected graph with integer edge weights, minimum spanning trees may not be unique. In this article, we present an algorithm that lists all the minimum spanning trees included in the graph. The computational complexity of the algorithm is O(N(mn+ n2 log n)) in time and O(m) in space, w...

Graphs with all spanning trees nonisomorphic

Listing All Plane Graphs

In this paper we give a simple algorithm to generate all connected rooted plane graphs with at most m edges. A “rooted” plane graph is a plane graph with one designated (directed) edge on the outer face. The algorithm uses O(m) space and generates such graphs in O(1) time per graph on average without duplications. The algorithm does not output the entire graph but the difference from the previo...

Spanning Tree Enumeration in 2-trees: Sequential and Parallel Perspective

For a connected graph, a vertex separator is a set of vertices whose removal creates at least two components. A vertex separator S is minimal if it contains no other separator as a strict subset and a minimum vertex separator is a minimal vertex separator of least cardinality. A clique is a set of mutually adjacent vertices. A 2-tree is a connected graph in which every maximal clique is of size...