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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 ...
Thus, while the Civil Code seeks to govern all aspects of private law in the Philippines, a Republic Act such as Republic Act No. 9048 would concern itself with a more limited field, as in that case, the correction of entries in the civil registry. Still, the amendment of Philippine legal codes is accomplished through the passage of Republic Acts.
Republic of Philippines v. Pimentel , [ note 1 ] 553 U.S. 851 (2008), is a decision of the Supreme Court of the United States which clarified the Federal Rules of Civil Procedure as regards money damages sought by a foreign government, the Republic of the Philippines , via its Presidential Commission on Good Government (PCGG).
In 2022, the firm received a Silver Anvil Award in the 57th Anvil Awards by the Public Relations Society of the Philippines. [17] Divina's law firm celebrated its 16th anniversary in April 2022. It has over 800 clients and handles almost 4,000 cases. [18] The firm also conducts free legal assistance through its program Dulog Legal, which was ...
A.C., [1] administrative case [2] N/A: English A case brought under administrative law in the form of a quasi-judicial proceeding by an agency of a non-judicial branch of government, or, the Office of the Court Administrator. Normally, such cases are internal disciplinary matters—court cases criminal and civil can be brought alongside them if ...
Trevor v Whitworth (1887) 12 App Cas 409 is a UK company law case concerning share buybacks. It held they were unlawful. The case is often used in support for the Capital Maintenance Rule. The rule coming from the case itself has since been reformed by statute in several commonwealth countries.