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  1. en.wikipedia.org › wiki › Orientation_(graph_theory)Orientation (graph theory) - Wikipedia

    Among directed graphs, the oriented graphs are the ones that have no 2-cycles (that is at most one of (x, y) and (y, x) may be arrows of the graph). [1] A tournament is an orientation of a complete graph. A polytree is an orientation of an undirected tree. [2] Sumner's conjecture states that every tournament with 2n – 2 vertices contains ...

  2. mathworld.wolfram.com › GraphOrientationGraph Orientation -- from Wolfram MathWorld

    6 days ago · An orientation of an undirected graph G is an assignment of exactly one direction to each of the edges of G. Only connected, bridgeless graphs can have a strong orientation (Robbins 1939; Skiena 1990, p. 174). An oriented complete graph is called a tournament.

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  4. mathonline.wikidot.com › orientable-graphsOrientable Graphs - Mathonline - Wikidot

    Orientable Graphs. Definition: A digraph D is said to be Orientable if there exists an orientation (a selection of arc directions) that makes D strongly connected (there exists a directed path between each pair of vertices). Definition: An Orientation of a graph G is the replacement of all edges {x, y} ∈ E(G) with either the arc (x, y) or (y, x).

  5. math.libretexts.org › Bookshelves › Combinatorics_and11.2: Basic Definitions, Terminology, and Notation

    Jul 12, 2021 · In a graph without loops, we can define the valency of any vertex \(v\) as the number of edges incident with \(v\). For most purposes, this is a good way to think of the valency. However, when a graph has loops, many formulas work out more nicely if we consider each loop to contribute \(2\) to the valency of its endvertex.

  6. en.wikipedia.org › wiki › Curve_orientationCurve orientation - Wikipedia

    Curve orientation. In mathematics, an orientation of a curve is the choice of one of the two possible directions for travelling on the curve. For example, for Cartesian coordinates, the x -axis is traditionally oriented toward the right, and the y -axis is upward oriented. In the case of a planar simple closed curve (that is, a curve in the ...

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  8. encyclopediaofmath.org › wiki › OrientationOrientation - Encyclopedia of Mathematics

    Jun 13, 2020 · In classical mathematics, an orientation is the choice of an equivalence class of coordinate systems, where two coordinate systems belong to the same class if they are positively related (in a specific sense). In the case of a finite-dimensional vector space $\R^n$, a coordinate system is given by a basis, and two bases are positively related ...

  9. theory.stanford.edu › ~megiddo › pdfDEFINITION - Stanford University

    DEFINITION 1.1. An orientation of an undirected graph G is a directed graph G' obtained from G by replacing each edge of G with a single directed edge. LINEAR ALGEBRA AND ITS APPLICATIONS 114/115:589-602 (1989) 589 0 Elsevier Science Publishing Co., Inc., 1989 655 Avenue of the Americas, New York, NY 10010

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