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In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points ) which are connected by edges (also called arcs , links or lines ).
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called vertices (also called nodes or points ) and each of the related pairs of vertices is called an edge (also called link or line ...
This is a list of graph theory topics, by Wikipedia page. See glossary of graph theory for basic terminology. ... Tree structure; Tree data structure; Cayley's formula;
The web graph W 4,2 is a cube. The web graph W n,r is a graph consisting of r concentric copies of the cycle graph C n, with corresponding vertices connected by "spokes". Thus W n,1 is the same graph as C n, and W n,2 is a prism. A web graph has also been defined as a prism graph Y n+1, 3, with the edges of the outer cycle removed. [7] [10]
In mathematics, they are useful in geometry and certain parts of topology, e.g. knot theory. Algebraic graph theory has close links with group theory and topological graph theory has close links to topology. There are also continuous graphs; however, for the most part, research in graph theory falls within the domain of discrete mathematics.
In Mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.
The axioms for the theory of graphs are Symmetric: ∀x ∀y R(x,y)→ R(y,x) Anti-reflexive: ∀x ¬R(x,x) ("no loops") The theory of random graphs has the following extra axioms for each positive integer n: For any two disjoint finite sets of size n, there is a point joined to all points of the first set and to no points of the second set.
Graph theory is the branch of mathematics that examines the properties of mathematical graphs.See glossary of graph theory for common terms and their definition.. Informally, this type of graph is a set of objects called vertices (or nodes) connected by links called edges (or arcs), which can also have associated directions.