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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 ]
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 ...
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 ...
The Constitution of the Philippines (Filipino: Saligang Batas ng Pilipinas or Konstitusyon ng Pilipinas) is the supreme law of the Philippines. Its final draft was completed by the Constitutional Commission on October 12, 1986, and ratified by a nationwide plebiscite on February 2, 1987. The Constitution remains unamended to this day.
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
The Tydings–McDuffie Act of the United States Government detailed the steps required for the Philippines to become independent of the United States. A previous act, the Hare–Hawes–Cutting Act, had been rejected by the Philippine Congress. The constitution was approved by 96% of voters, and was replaced by the 1973 Constitution of the ...
The Tydings–McDuffie Act specified a procedural framework for the drafting of a constitution for the government of the Commonwealth of the Philippines within two years of its enactment. The act specified a number of mandatory constitutional provisions, and required approval of the constitution by the U.S. President and by Filipinos.
After the constitution was approved by 95% of the voters in the Philippine constitutional plebiscite, the 1935 Constitution was replaced with a new one that changed the system of government from a presidential to a parliamentary one, with Marcos remaining in power as both head of state (with the title "President") and head of government (titled ...