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In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. [1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees.
The Cayley graph of a free group of finite rank, with respect to a free generating set, is a tree on which the group acts freely, preserving the orientation. As a topological space (a one-dimensional simplicial complex), this Cayley graph Γ(F) is contractible.
The complete list of all trees on 2,3,4 labeled vertices: = tree with 2 vertices, = trees with 3 vertices and = trees with 4 vertices. In mathematics, Cayley's formula is a result in graph theory named after Arthur Cayley.
Note that simply running classical Prim's on a graph with random edge weights would create mazes stylistically identical to Kruskal's, because they are both minimal spanning tree algorithms. Instead, this algorithm introduces stylistic variation because the edges closer to the starting point have a lower effective weight.
Binary tree generated in Graphviz from a DOT description by an online Huffman Tree generator. The DOT language defines a graph, but does not provide facilities for rendering the graph. There are several programs that can be used to render, view, and manipulate graphs in the DOT language:
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, [1] is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley ), and uses a specified set of generators for the group.