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Encyclopedia > Graph properties

In mathematics a graph invariant or graph property is one of the basic properties of graphs studied in graph theory. Mathematics, often abbreviated maths in Commonwealth English and math in American English, is the study of abstraction. ... In mathematics and computer science, graph theory studies the properties of graphs. ...


A graph can be given graphically in the form of a graph drawing. But a given graph may be drawn in several equivalent ways and even for small graphs it is often hard to decide if two drawings represent the same graph, that is if two graphs are isomorphic. Graphs are often represented pictorially as follows: draw a dot for every vertex, and for every edge draw an arc connecting its endpoints. ... In the mathematical field of graph theory a graph homomorphism is a mapping between two graphs that respects their structure. ...


When manipulating graphs in a computer, depending on the data structure used, the vertices and the edges of the graph have to be labeled. There is no canonical way to label a graph and a common problem is to decide if two graph structures are isomorphic. In computer science, a graph is an abstract data type (ADT) that consists of a set of nodes and a set of edges that establish relationships (connections) between the nodes. ... This article just presents the basic definitions. ... This article just presents the basic definitions. ... In the mathematical discipline of graph theory, a graph labeling is the assignment of unique identifiers to the edges and vertices of a graph. ...


Proving that two given graph presentations are not isomorphic is often done by showing that one graph has a certain graph invariant the other graph lacks.


Graph invariants

  • number of vertices
  • number of edges

  Results from FactBites:
 
Graph theory - Wikipedia, the free encyclopedia (1213 words)
Informally, a graph is a set of objects called vertices (or nodes) connected by links called edges (or arcs) which can be directed (assigned a direction).
Graphs are represented graphically by drawing a dot for every vertex, and drawing an arc between two vertices if they are connected by an edge.
Firstly, analysis to determine structural properties of a network, such as whether or not it is a scale-free network, or a small-world network.
ASP Component to draw pie charts, bar charts and line graphs with ASP - online instructions. (8391 words)
When these properties are not specified in code they will take their default values and these defaults have been selected with the aim of producing a legible graph with the minimum of code.
Properties are available to specify the position of the pie and its diameter, as well as options for showing the data values and/or the labels (data item names).
Properties have been provided in the section on line graphs to allow a prefix, suffix or separator to be applied to a single axis.
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