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In graph theory, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch an odd number of edges is even. For example, if there is a party of people who shake hands, the number of people who shake an odd number of other people's hands is even. [ 1 ]
According to the research page, this research has the potential of resolving the still unresolved theory of six degrees of separation. [ 23 ] [ 35 ] Facebook's data team released two papers in November 2011 which document that amongst all Facebook users at the time of research (721 million users with 69 billion friendship links) there is an ...
In set theory and graph theory, denotes the set of n-tuples of elements of , that is, ordered sequences of elements that are not necessarily distinct. In the edge ( x , y ) {\displaystyle (x,y)} directed from x {\displaystyle x} to y {\displaystyle y} , the vertices x {\displaystyle x} and y {\displaystyle y} are called the endpoints of the ...
Pages in category "Theorems in graph theory" The following 54 pages are in this category, out of 54 total. ... Kőnig's theorem (graph theory) Kotzig's theorem ...
This hand-shaking example is equivalent to the statement that in any graph with more than one vertex, there is at least one pair of vertices that share the same degree. [8] This can be seen by associating each person with a vertex and each edge with a handshake. [citation needed]
In the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or n-fan) F n is a planar, undirected graph with 2n + 1 vertices and 3n edges. [ 1 ] The friendship graph F n can be constructed by joining n copies of the cycle graph C 3 with a common vertex, which becomes a universal vertex for the graph.
Nunberg believes his handshake is indicative of Trump's famous phrase, too. He told Huffington Post, "If we are talking about his handshake, it is kind of analogous to us talking about him when he ...
A graph with a loop having vertices labeled by degree. In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex; in a multigraph, a loop contributes 2 to a vertex's degree, for the two ends of the edge. [1]