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2. Tree (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Tree_(graph_theory)

   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.

3. Polytree - Wikipedia

   en.wikipedia.org/wiki/Polytree

   A polytree. In mathematics, and more specifically in graph theory, a polytree [1] (also called directed tree, [2] oriented tree [3] or singly connected network [4]) is a directed acyclic graph whose underlying undirected graph is a tree.

4. Graph theory - Wikipedia

   en.wikipedia.org/wiki/Graph_theory

   In mathematics and computer science, graph theory is the study ... forms arising from differential calculus to study a particular class of graphs, the trees. ...

5. Caterpillar tree - Wikipedia

   en.wikipedia.org/wiki/Caterpillar_tree

   A k-tree is a chordal graph with exactly n − k maximal cliques, each containing k + 1 vertices; in a k-tree that is not itself a (k + 1)-clique, each maximal clique either separates the graph into two or more components, or it contains a single leaf vertex, a vertex that belongs to only a single maximal clique.

6. Graph (discrete mathematics) - Wikipedia

   en.wikipedia.org/wiki/Graph_(discrete_mathematics)

   A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).

7. Graph of groups - Wikipedia

   en.wikipedia.org/wiki/Graph_of_groups

   It is possible to define a graph with vertices and edges the disjoint union of all coset spaces Γ/G x and Γ/G y respectively. This graph is a tree, called the universal covering tree, on which Γ acts. It admits the graph Y as fundamental domain. The graph of groups given by the stabilizer subgroups on the fundamental domain corresponds to ...

8. Spanning tree - Wikipedia

   en.wikipedia.org/wiki/Spanning_tree

   As with finite graphs, a tree is a connected graph with no finite cycles, and a spanning tree can be defined either as a maximal acyclic set of edges or as a tree that contains every vertex. [ 27 ] The trees within a graph may be partially ordered by their subgraph relation, and any infinite chain in this partial order has an upper bound (the ...

9. Complete graph - Wikipedia

   en.wikipedia.org/wiki/Complete_graph

   The complement graph of a complete graph is an empty graph. If the edges of a complete graph are each given an orientation, the resulting directed graph is called a tournament. K n can be decomposed into n trees T i such that T i has i vertices. [6] Ringel's conjecture asks if the complete graph K 2n+1 can be decomposed into copies of any tree ...