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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
President Aquino later issued Proclamation No. 9, creating a Constitutional Commission (popularly abbreviated as "ConCom" in the Philippines) to frame a new constitution to replace the 1973 Constitution, which took effect during the martial law regime of her predecessor. President Aquino appointed 50 members to the Commission.
The government of the Philippines (Filipino: Pamahalaan ng Pilipinas) has three interdependent branches: the legislative, executive, and judicial branches.The Philippines is governed as a unitary state under a presidential representative and democratic constitutional republic in which the president functions as both the head of state and the head of government of the country within a pluriform ...
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 ...