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However, it is possible to formulate a version of the handshaking lemma using the concept of an end, an equivalence class of semi-infinite paths ("rays") considering two rays as equivalent when there exists a third ray that uses infinitely many vertices from each of them. The degree of an end is the maximum number of edge-disjoint rays that it ...
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 ...
From the handshaking lemma, a k-regular graph with odd k has an even number of vertices. A theorem by Nash-Williams says that every k ‑regular graph on 2k + 1 vertices has a Hamiltonian cycle. Let A be the adjacency matrix of a graph. Then the graph is regular if and only if = (, …,) is an eigenvector of A. [2]
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
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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 ...
Mazur's torsion theorem (algebraic geometry) Mean value theorem ; Measurable Riemann mapping theorem (conformal mapping) Mellin inversion theorem (complex analysis) Menelaus's theorem ; Menger's theorem (graph theory) Mercer's theorem (functional analysis) Mermin–Wagner theorem ; Mertens's theorems (number theory)