For the network protocol, see Spanning Tree Protocol. For other uses, see Spanning tree (disambiguation).
A spanning tree (blue heavy edges) of a grid graph
In the mathematical field of graph theory, a spanning treeT of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G.[1] In general, a graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree (see about spanning forests below). If all of the edges of G are also edges of a spanning tree T of G, then G is a tree and is identical to T (that is, a tree has a unique spanning tree and it is itself).
^"Tree". NetworkX 2.6.2 documentation. Retrieved 2021-12-10. For trees and arborescence, the adjective "spanning" may be added to designate that the graph, when considered as a forest/branching, consists of a single tree/arborescence that includes all nodes in the graph.
graph may have several spanningtrees, but a graph that is not connected will not contain a spanningtree (see about spanning forests below). If all of...
The SpanningTree Protocol (STP) is a network protocol that builds a loop-free logical topology for Ethernet networks. The basic function of STP is to...
minimum spanning forest, which is a union of the minimum spanningtrees for its connected components. There are many use cases for minimum spanningtrees. One...
Wikimedia Commons has media related to Multiple SpanningTree Protocol. The Multiple SpanningTree Protocol (MSTP) and algorithm, provides both simple...
A Euclidean minimum spanningtree of a finite set of points in the Euclidean plane or higher-dimensional Euclidean space connects the points by a system...
In mathematics, a random minimum spanningtree may be formed by assigning independent random weights from some distribution to the edges of an undirected...
good spanningtree T {\displaystyle T} of an embedded planar graph G {\displaystyle G} is a rooted spanningtree of G {\displaystyle G} whose non-tree edges...
In graph theory, a minimum degree spanningtree is a subset of the edges of a connected graph that connects all the vertices together, without any cycles...
weighted edge in a spanningtree. A spanningtree is a minimum bottleneck spanningtree if the graph does not contain a spanningtree with a smaller bottleneck...
distance spanningtree, shortest total path length spanningtree, minimum total distance spanningtree, or minimum average distance spanningtree. In an...
A kinetic minimum spanningtree is a kinetic data structure that maintains the minimum spanningtree (MST) of a graph whose edge weights are changing as...
the (non-negative) shortest path problem and the minimum spanningtree problem. If a Steiner tree problem in graphs contains exactly two terminals, it reduces...
Linear spanning, a concept in abstract algebra Spanningtree, a subgraph which is a tree, containing all the vertices of a graph Søren Spanning (1951–2020)...
now know as the internet. She is most famous for her invention of the SpanningTree Protocol (STP), which is fundamental to the operation of network bridges...
random tree is a tree or arborescence that is formed by a stochastic process. Types of random trees include: Uniform spanningtree, a spanningtree of a...
for an Expected Linear-Time Minimum SpanningTree Algorithm(Karger-Klein-Tarjan + Hagerup Minimum SpanningTree Verification as a sub-routine)". GitHub...
the edges of which is lowest among all spanningtrees of G {\displaystyle G} , is called a minimum spanningtree (MST). It is not necessarily unique. More...
The distributed minimum spanningtree (MST) problem involves the construction of a minimum spanningtree by a distributed algorithm, in a network where...
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