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In graph theory, the girth of an undirected graph is the length of a shortest cycle contained in the graph. [1] If the graph does not contain any cycles (that is, it is a forest), its girth is defined to be infinity. [2] For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3.
The firm produces at the quantity of output where marginal cost equals marginal revenue (labeled Q in the upper graph), and its per-unit economic profit is the difference between average revenue AR and average total cost ATC at that point, the difference being P minus C in the graph's notation. With firms making economic profit and with free ...
The graph shown here appears as a subgraph of an undirected graph if and only if models the sentence ,,,... In the first-order logic of graphs, a graph property is expressed as a quantified logical sentence whose variables represent graph vertices, with predicates for equality and adjacency testing.
A drawing of a graph with 6 vertices and 7 edges.. In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
An example graph, with the properties of being planar and being connected, and with order 6, size 7, diameter 3, girth 3, vertex connectivity 1, and degree sequence <3, 3, 3, 2, 2, 1> In graph theory , a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations such as ...
Equivalently, each edge in the graph has at most one endpoint in . A set is independent if and only if it is a clique in the graph's complement. The size of an independent set is the number of vertices it contains. Independent sets have also been called "internally stable sets", of which "stable set" is a shortening. [1]
The market structure determines the price formation method of the market. Suppliers and Demanders (sellers and buyers) will aim to find a price that both parties can accept creating a equilibrium quantity. Market definition is an important issue for regulators facing changes in market structure, which needs to be determined. [1]
In a connected graph, each cut-set determines a unique cut, and in some cases cuts are identified with their cut-sets rather than with their vertex partitions. In a flow network , an s–t cut is a cut that requires the source and the sink to be in different subsets, and its cut-set only consists of edges going from the source's side to the ...