Contents. 1 I DEFINITIONS AND FUNDAMENTAL CONCEPTS an introduction to basic concepts and results in graph theory, with a special emphasis put on. A graph G is a triple consisting of a vertex set of V(G), an edge set E(G), and a For a set S Í V, the open neighborhood N(S) is defined to be UvÎSN(v), and the. Graph Theory Definitions. A graph is a pair of sets (V,E) where V is a finite set called the set of vertices and E is a set of 2-element. subsets of V, called the set of edges. We view the edges as a set of connections between the nodes.


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Graph theory - Wikipedia

An arc is a directed line a pair of ordered vertices. An edge is line joining a pair of nodes. Incident edges are edges which share a vertex.


A edge and vertex are incident if the edge connects the vertex to another. A loop is an edge or arc that joins a vertex to itself. A vertex, sometimes called a node, is a point or circle. A graph theory definitions G is connected if there is a path in G between any given pair of vertices, otherwise it is disconnected.

Every disconnected graph can be graph theory definitions up into a number of connected subgraphs, called components.

What is graph theory? - Definition from

In particular, the term "graph" was introduced by Sylvester in a paper published in in Naturewhere he draws an analogy between "quantic invariants" graph theory definitions "co-variants" of algebra and molecular diagrams: Many incorrect proofs have been proposed, including those by Cayley, Kempeand others.

The study and the generalization of this problem by TaitHeawoodRamsey and Hadwiger led to the study of the colorings of the graphs embedded on surfaces with arbitrary genus. The four color graph theory definitions remained unsolved for more than a century. In Heinrich Heesch published a method for solving the problem using computers.

A simpler proof considering only configurations was given twenty years later by RobertsonSeymourSanders and Thomas. Another important factor of common development of graph theory and topology came from the use of the techniques of modern algebra.

Graph theory definitions first example of such a use comes from the work of the physicist Gustav Kirchhoffwho published in his Kirchhoff's circuit laws for calculating the voltage and current in electric circuits.

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Graph drawing Graphs are represented visually by drawing a dot or circle for every vertex, and drawing an arc between two vertices if they are connected by an edge. If the graph is directed, the direction is indicated by drawing an arrow.

A graph drawing should not be confused with the graph itself the abstract, non-visual structure as there are several ways to structure the graph drawing.

All that matters is which vertices are connected to which others by how graph theory definitions edges and not the exact layout. In practice, graph theory definitions is often difficult to decide if two drawings represent the same graph.

Graph Theory: Definition and Properties

Depending on the problem domain some layouts may be better suited and easier to understand than others. The pioneering work of W. For instance, the road transportation network of a city is a sub-graph of a regional transportation network, which is itself a sub-graph of a national transportation network.

Graph theory definitions Loop or self edge. A link that makes a node correspond to itself graph theory definitions a buckle.

A graph where all the intersections of graph theory definitions edges are a vertex. Since this graph is located within a plane, its topology is two-dimensional. This is typically graph theory definitions case for power grids, road and railway networks, although great care must be inferred to the definition of nodes terminals, warehouses, cities.


A graph where there are no vertices at the graph theory definitions of at least two edges. Networks that can be considered in a planar fashion, such as roads, can be represented as non-planar networks.

Definition of Graph Theory | What is Graph Theory ? Graph Theory Meaning - The Economic Times

A non-planar graph has potentially much more links graph theory definitions a planar graph. It has a direction that is generally represented as an arrow. If an arrow is not used, it means the link is bi-directional.

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