Pronunciation: [spˈan tɹˈiː] (IPA) 
The correct spelling of "span tree" is actually "spanning tree" /ˈspænɪŋ triː/. The word "spanning" is spelled with double 'n' instead of a single 'n'. The IPA phonetic transcription for "spanning" is /ˈspænɪŋ/. Meanwhile, "tree" is spelled as it is since it follows the basic English spelling rules. The IPA phonetic transcription for "tree" is /triː/. A spanning tree is a tree-like subgraph of a connected, undirected graph.
A spanning tree can be defined as a subset of a graph that contains all the vertices of the original graph, yet forms a tree structure without any cycles. In other words, a spanning tree is a connected, acyclic subgraph of a given graph G.
To clarify, a graph represents a collection of vertices and edges, where vertices denote distinct points and edges connect these points. The graph can be directed (where edges have a specific origin and destination) or undirected (where edges have no direction).
When a spanning tree is formed, it must satisfy two fundamental properties: it spans all the vertices of the original graph and has a minimum possible number of edges. Hence, a spanning tree is the smallest possible connected subgraph of the original graph.
Spanning trees have numerous applications in various fields, including computer science, network design, and transportation planning. For instance, in network design, a spanning tree ensures that every node in a network is reachable without any loops or redundant connections. This makes it useful for optimizing data transmission and preventing excessive traffic.
It is crucial to note that a graph may have multiple spanning trees. Different algorithms can be applied to find a minimum or maximum spanning tree based on specific requirements, such as weighting edges or minimizing costs.
The term "span tree" does not have a specific etymology in and of itself. It is a combination of two words: "span" and "tree", each with its own etymology.
1. "Span":
The word "span" derives from Middle English and Old Norse origins. In Old Norse, "spann" meant "to measure by the span of the hand". In Middle English, it referred to the gesture of stretching out one's hand to its fullest extent, indicating a measure of distance. Over time, "span" came to mean the distance between the thumb and little finger when the hand is fully extended, which is roughly equivalent to nine inches.
2. "Tree":
The word "tree" comes from Old English "treow", which can be traced back to prehistoric Germanic languages. It originally referred to any large, woody plant.
