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  2. Tree (graph theory) - Wikipedia

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

    A star tree is a tree which consists of a single internal vertex (and n – 1 leaves). In other words, a star tree of order n is a tree of order n with as many leaves as possible. A caterpillar tree is a tree in which all vertices are within distance 1 of a central path subgraph.

  3. Leaf power - Wikipedia

    en.wikipedia.org/wiki/Leaf_power

    A tree (top) and its corresponding 3-leaf power (bottom) In the mathematical area of graph theory, a k-leaf power of a tree T is a graph G whose vertices are the leaves of T and whose edges connect pairs of leaves whose distance in T is at most k. That is, G is an induced subgraph of the graph power ⁠ ⁠, induced by the leaves of T.

  4. Tree structure - Wikipedia

    en.wikipedia.org/wiki/Tree_structure

    A tree structure, tree diagram, or tree model is a way of representing the hierarchical nature of a structure in a graphical form. It is named a "tree structure" because the classic representation resembles a tree , although the chart is generally upside down compared to a biological tree, with the "stem" at the top and the "leaves" at the bottom.

  5. Glossary of graph theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_graph_theory

    1. A leaf vertex or pendant vertex (especially in a tree) is a vertex whose degree is 1. A leaf edge or pendant edge is the edge connecting a leaf vertex to its single neighbour. 2. A leaf power of a tree is a graph whose vertices are the leaves of the tree and whose edges connect leaves whose distance in the tree is at most a given threshold.

  6. File:Leaf, Bud, and Stem Diagram.svg - Wikipedia

    en.wikipedia.org/wiki/File:Leaf,_Bud,_and_Stem...

    English: This diagram show a specific parts of a leaf that is on a stem. The parts included are: 1. Apex 2. Midvein (Primary vein) 3. Secondary vein. 4. Lamina. 5. Leaf margin 6. Petiole 7. Bud 8. Stem

  7. Real tree - Wikipedia

    en.wikipedia.org/wiki/Real_tree

    Here are equivalent characterizations of real trees which can be used as definitions: 1) (similar to trees as graphs) A real tree is a geodesic metric space which contains no subset homeomorphic to a circle. [1] 2) A real tree is a connected metric space (,) which has the four points condition [2] (see figure):

  8. Vertex (graph theory) - Wikipedia

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

    A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...

  9. 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.

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