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• 1998 AIME Problems/Problem 15
  ...x, so every vertex reached is equivalent to adding 2 more segments. So the degree of each vertex must be even, with the exception of endpoints) Since there a In the language of graph theory, this is an example of an Eulerian circuit.
  9 KB (1,659 words) - 17:35, 20 June 2024
• Degree
  * [[Degree (geometry)]], the degrees in an [[angle]]. ...(graph theory)]], the degree of a [[vertex]] in a [[graph (graph theory) | graph]].
  233 bytes (33 words) - 18:26, 30 January 2007
• Graph (graph theory)
  In [[graph theory]], a '''graph''' is a (usually [[finite]]) [[empty set | nonempty]] [[set]] of [[vertex|v Formally, a graph <math>G</math> is a pair, <math>G = (V, E)</math>, of a set <math>V</math>
  8 KB (1,428 words) - 09:26, 27 August 2020
• Directed graph
  A '''directed graph''' (sometimes abbreviated ''digraph'') is a [[graph]] in which each [[edge]] is assigned an orientation. Formally, a digraph < ...in E\right\}</math>. A digraph is usually drawn by drawing the underlying graph and putting an arrow on each edge to indicate the direction.
  4 KB (688 words) - 17:39, 24 February 2025
• 2008 USAMO Problems/Problem 6
  Make the obvious re-interpretation as a [[graph]]. Let <math>f : G \to \{0,1\}</math> be an [[indicator function]] with <ma ...partition [[iff]] <math>(Af)(v) = d(v)</math>, where <math>d</math> is the degree of <math>v</math>, for all <math>v</math> (this is taken over <math>F_2</ma
  13 KB (2,414 words) - 13:37, 11 July 2016
• 2019 AMC 12B Problems/Problem 10
  ==Solution 1 (graph theory)== ...ath> edges coming into/out of them (i.e., in graph theory terms, they have degree <math>3</math>). Therefore, at least <math>1</math> edge connecting to each
  8 KB (1,306 words) - 21:18, 1 February 2020
• 2005 Indonesia MO Problems/Problem 8
  ...ctions and self connections are not allowed and therefore that the maximum degree of any given vertex is 89. In the limiting case, the degree sequence of the graph is <math>60, 60, 60,
  3 KB (508 words) - 18:58, 3 February 2024
• Matrix Tree Theorem
  ...Graph Theory]] that counts for the number of spanning trees of a connected graph. It was discovered by Gustav Kirchhoff, which is why the theorem is also c Let <math>G</math> be a graph with the set of vertices <math>V=\{v_1,v_2,v_3,\ldots, v_n\}</math>. We de
  1 KB (264 words) - 10:26, 3 March 2022