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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 ]
The formula implies that in any undirected graph, the number of vertices with odd degree is even. This statement (as well as the degree sum formula) is known as the handshaking lemma. The latter name comes from a popular mathematical problem, which is to prove that in any group of people, the number of people who have shaken hands with an odd ...
In more colloquial terms, in a party of people some of whom shake hands, an even number of people must have shaken an odd number of other people's hands; for this reason, the result is known as the handshaking lemma. To prove this by double counting, let () be the degree of vertex . The number of vertex-edge incidences in the graph may be ...
Burnside's lemma also known as the Cauchy–Frobenius lemma; Frattini's lemma (finite groups) Goursat's lemma; Mautner's lemma (representation theory) Ping-pong lemma (geometric group theory) Schreier's subgroup lemma; Schur's lemma (representation theory) Zassenhaus lemma
President Donald Trump signed an executive order Tuesday to end federal support for medical procedures aimed at altering sex or gender that involve surgical interventions or the use of puberty ...
Handshake may also refer to: Handshake (computing), a computing term related to automated communication between two computing devices or programs [disputed (for: There are many other types of handshaking in computing.) – discuss] Handshake deal, another term for an oral contract; Handshaking lemma, a specific statement in graph theory
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 ...
Handshaking lemma; K. Kőnig's lemma; S. Szemerédi regularity lemma This page was last edited on 21 February 2021, at 00:40 (UTC). Text is available under the ...