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  2. Ordered graph - Wikipedia

    en.wikipedia.org/wiki/Ordered_graph

    The induced graph of an ordered graph is obtained by adding some edges to an ordering graph, using the method outlined below. The induced width of an ordered graph is the width of its induced graph. [2] Given an ordered graph, its induced graph is another ordered graph obtained by joining some pairs of nodes that are both parents of another node.

  3. Graph (discrete mathematics) - Wikipedia

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

    A path graph or linear graph of order n ≥ 2 is a graph in which the vertices can be listed in an order v 1, v 2, …, v n such that the edges are the {v i, v i+1} where i = 1, 2, …, n − 1. Path graphs can be characterized as connected graphs in which the degree of all but two vertices is 2 and the degree of the two remaining vertices is 1.

  4. Topological sorting - Wikipedia

    en.wikipedia.org/wiki/Topological_sorting

    An alternative algorithm for topological sorting is based on depth-first search.The algorithm loops through each node of the graph, in an arbitrary order, initiating a depth-first search that terminates when it hits any node that has already been visited since the beginning of the topological sort or the node has no outgoing edges (i.e., a leaf node):

  5. Perfectly orderable graph - Wikipedia

    en.wikipedia.org/wiki/Perfectly_orderable_graph

    Equivalently, these are the graphs in which the partial order of closed neighborhoods, ordered by set inclusion, has width at most four. The 5-vertex cycle graph has a neighborhood partial order of width five, so four is the maximum width that ensures perfect orderability. As with the chordal graphs (and unlike the perfectly orderable graphs ...

  6. Graph theory - Wikipedia

    en.wikipedia.org/wiki/Graph_theory

    A directed graph or digraph is a graph in which edges have orientations. In one restricted but very common sense of the term, [5] a directed graph is an ordered pair = (,) comprising: , a set of vertices (also called nodes or points);

  7. Partially ordered set - Wikipedia

    en.wikipedia.org/wiki/Partially_ordered_set

    The vertex set of a directed acyclic graph ordered by reachability. The set of subspaces of a vector space ordered by inclusion. For a partially ordered set P, the sequence space containing all sequences of elements from P, where sequence a precedes sequence b if every item in a precedes the corresponding item in b.

  8. Directed graph - Wikipedia

    en.wikipedia.org/wiki/Directed_graph

    In formal terms, a directed graph is an ordered pair G = (V, A) where [1]. V is a set whose elements are called vertices, nodes, or points;; A is a set of ordered pairs of vertices, called arcs, directed edges (sometimes simply edges with the corresponding set named E instead of A), arrows, or directed lines.

  9. Order (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Order_(mathematics)

    Graph order, the number of nodes in a graph; First order and second order logic of graphs; Topological ordering of directed acyclic graphs; Degeneracy ordering of undirected graphs; Elimination ordering of chordal graphs; Order, the complexity of a structure within a graph: see haven (graph theory) and bramble (graph theory)

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