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  2. Euler tour technique - Wikipedia

    en.wikipedia.org/wiki/Euler_tour_technique

    The Euler tour technique (ETT), named after Leonhard Euler, is a method in graph theory for representing trees. The tree is viewed as a directed graph that contains two directed edges for each edge in the tree. The tree can then be represented as a Eulerian circuit of the directed graph, known as the Euler tour representation (ETR) of the tree

  3. Biological network - Wikipedia

    en.wikipedia.org/wiki/Biological_network

    Euler's objective was to design a path that crossed each bridge only once. As early as 1736 Leonhard Euler analyzed a real-world issue known as the Seven Bridges of Königsberg, which established the foundation of graph theory. From the 1930s-1950s the study of random graphs were developed.

  4. Tree of life (biology) - Wikipedia

    en.wikipedia.org/wiki/Tree_of_life_(biology)

    The tree of life or universal tree of life is a metaphor, conceptual model, and research tool used to explore the evolution of life and describe the relationships between organisms, both living and extinct, as described in a famous passage in Charles Darwin's On the Origin of Species (1859). [1]

  5. Euler diagram - Wikipedia

    en.wikipedia.org/wiki/Euler_diagram

    For example, connectedness of zones might be enforced, or concurrency of curves or multiple points might be banned, as might tangential intersection of curves. In the adjacent diagram, examples of small Venn diagrams are transformed into Euler diagrams by sequences of transformations; some of the intermediate diagrams have concurrency of curves.

  6. Euler characteristic - Wikipedia

    en.wikipedia.org/wiki/Euler_characteristic

    The Euler characteristic can be defined for connected plane graphs by the same + formula as for polyhedral surfaces, where F is the number of faces in the graph, including the exterior face. The Euler characteristic of any plane connected graph G is 2.

  7. Eulerian path - Wikipedia

    en.wikipedia.org/wiki/Eulerian_path

    An Eulerian trail, [note 1] or Euler walk, in an undirected graph is a walk that uses each edge exactly once. If such a walk exists, the graph is called traversable or semi-eulerian. [3] An Eulerian cycle, [note 1] also called an Eulerian circuit or Euler tour, in an undirected graph is a cycle that uses each edge exactly once

  8. Planar graph - Wikipedia

    en.wikipedia.org/wiki/Planar_graph

    Euler's formula can also be proved as follows: if the graph isn't a tree, then remove an edge which completes a cycle. This lowers both e and f by one, leaving v – e + f constant. 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.

  9. Phylogenetic tree - Wikipedia

    en.wikipedia.org/wiki/Phylogenetic_tree

    The idea of a tree of life arose from ancient notions of a ladder-like progression from lower into higher forms of life (such as in the Great Chain of Being).Early representations of "branching" phylogenetic trees include a "paleontological chart" showing the geological relationships among plants and animals in the book Elementary Geology, by Edward Hitchcock (first edition: 1840).