Distance (graph theory)In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance or shortest-path distance. Notice that there may be more than one shortest path between two vertices. If there is no path connecting the two vertices, i.e., if they belong to different connected components, then conventionally the distance is defined as infinite.
Spanning treeIn the mathematical field of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G. In general, a graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree (see about spanning forests below). If all of the edges of G are also edges of a spanning tree T of G, then G is a tree and is identical to T (that is, a tree has a unique spanning tree and it is itself).
Cycle (graph theory)In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is a non-empty directed trail in which only the first and last vertices are equal. A graph without cycles is called an acyclic graph. A directed graph without directed cycles is called a directed acyclic graph. A connected graph without cycles is called a tree. A circuit is a non-empty trail in which the first and last vertices are equal (closed trail).
Regular graphIn graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each internal vertex are equal to each other. A regular graph with vertices of degree k is called a k‐regular graph or regular graph of degree k. Also, from the handshaking lemma, a regular graph contains an even number of vertices with odd degree.
Greedy algorithmA greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locally optimal solutions that approximate a globally optimal solution in a reasonable amount of time. For example, a greedy strategy for the travelling salesman problem (which is of high computational complexity) is the following heuristic: "At each step of the journey, visit the nearest unvisited city.
Exchange rateIn finance, an exchange rate is the rate at which one currency will be exchanged for another currency. Currencies are most commonly national currencies, but may be sub-national as in the case of Hong Kong or supra-national as in the case of the euro. The exchange rate is also regarded as the value of one country's currency in relation to another currency. For example, an interbank exchange rate of 131 Japanese yen to the United States dollar means that ¥131 will be exchanged for or that will be exchanged for ¥131.
United States dollarThe United States dollar (symbol: ;currencycode:USD;alsoabbreviatedUS to distinguish it from other dollar-denominated currencies; referred to as the dollar, U.S. dollar, American dollar, or colloquially buck) is the official currency of the United States and several other countries. The Coinage Act of 1792 introduced the U.S. dollar at par with the Spanish silver dollar, divided it into 100 cents, and authorized the minting of coins denominated in dollars and cents. U.S. Exchange rate regimeAn exchange rate regime is a way a monetary authority of a country or currency union manages the currency about other currencies and the foreign exchange market. It is closely related to monetary policy and the two are generally dependent on many of the same factors, such as economic scale and openness, inflation rate, the elasticity of the labor market, financial market development, and capital mobility. There are two major regime types: Floating (or flexible) exchange rate regime exist where exchange rates are determined solely by market forces and often manipulated by open-market operations.
CurrencyA currency is a standardization of money in any form, in use or circulation as a medium of exchange, for example banknotes and coins. A more general definition is that a currency is a system of money in common use within a specific environment over time, especially for people in a nation state. Under this definition, the British Pound Sterling (£), euros (€), Japanese yen (¥), and U.S. dollars (US$) are examples of (government-issued) fiat currencies.
