Abstract
<h2>Abstract</h2> Spanning trees are fundamental objects in graph theory. The spanning tree set size of an arbitrary graph can be very large. This limitation discourages its analysis. However interesting patterns can emerge in small cases. In this article we introduce <i>tinygarden</i>, a java package for validating hypothesis, testing properties and discovering patterns from the spanning tree set of an arbitrary graph.
Highlights
Graph theory is a longstanding and well-established area of discrete mathematics
Spanning trees are important in optimization [1], network design [2], VLSI interconnection [3], clustering [4], complexity theory [5], graph invariants [6], fundamental cycle bases [7] and in many more areas of applied and theoretical sciences
The spanning tree set of an arbitrary graph can be very large [8]
Summary
Graph theory is a longstanding and well-established area of discrete mathematics. Graphs are abstract models of pairwise relations between entities in some domain. A cycle in G is a non-empty path in which the only repeated nodes are the first and last (see Fig. 3). A tree is a connected graph without cycles. A spanning tree T ⊆ G is a tree that contains all the nodes of G (see Fig. 4). Spanning trees are important in optimization [1], network design [2], VLSI interconnection [3], clustering [4], complexity theory [5], graph invariants [6], fundamental cycle bases [7] and in many more areas of applied and theoretical sciences. The spanning tree set of an arbitrary graph can be very large [8] This limit prevents the entire set from being explored. Since a Graph can be built based on a text file containing its incidence matrix, it works well together with nauty [12], the well-known graph software
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