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2. Treemapping - Wikipedia

   en.wikipedia.org/wiki/Treemapping

   In information visualization and computing, treemapping is a method for displaying hierarchical data using nested figures, usually rectangles. Treemaps display hierarchical (tree-structured) data as a set of nested rectangles. Each branch of the tree is given a rectangle, which is then tiled with smaller rectangles representing sub-branches.

3. Kruskal's tree theorem - Wikipedia

   en.wikipedia.org/wiki/Kruskal's_tree_theorem

   The version given here is that proven by Nash-Williams; Kruskal's formulation is somewhat stronger. All trees we consider are finite. Given a tree T with a root, and given vertices v, w, call w a successor of v if the unique path from the root to w contains v, and call w an immediate successor of v if additionally the path from v to w contains no other vertex.

4. Tree (graph theory) - Wikipedia

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

   v − 1. Chromatic number. 2 if v > 1. Table of graphs and parameters. 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 ...

5. Tree decomposition - Wikipedia

   en.wikipedia.org/wiki/Tree_decomposition

   In graph theory, a tree decomposition is a mapping of a graph into a tree that can be used to define the treewidth of the graph and speed up solving certain computational problems on the graph. Tree decompositions are also called junction trees, clique trees, or join trees. They play an important role in problems like probabilistic inference ...

6. Collatz conjecture - Wikipedia

   en.wikipedia.org/wiki/Collatz_conjecture

   Then the formula for the map is exactly the same as when the domain is the integers: an 'even' such rational is divided by 2; an 'odd' such rational is multiplied by 3 and then 1 is added. A closely related fact is that the Collatz map extends to the ring of 2-adic integers, which contains the ring of rationals with odd denominators as a subring.

7. Graph theory - Wikipedia

   en.wikipedia.org/wiki/Graph_theory

   In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links or lines).

8. Planar graph - Wikipedia

   en.wikipedia.org/wiki/Planar_graph

   Repeat until the remaining graph is a tree; trees have v = e + 1 and f = 1, yielding v – e + f = 2, i. e., the Euler characteristic is 2. In a finite, connected , simple , planar graph, any face (except possibly the outer one) is bounded by at least three edges and every edge touches at most two faces; using Euler's formula, one can then show ...

9. Cayley's formula - Wikipedia

   en.wikipedia.org/wiki/Cayley's_formula

   Cayley's formula immediately gives the number of labelled rooted forests on n vertices, namely (n + 1)n − 1. Each labelled rooted forest can be turned into a labelled tree with one extra vertex, by adding a vertex with label n + 1 and connecting it to all roots of the trees in the forest. There is a close connection with rooted forests and ...