In the mathematical discipline of graph theory, a graph labeling is the assignment of unique identifiers to the edges and vertices of a graph. Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of figures and numbers. Mathematical knowledge is constantly growing, through research and application, but mathematics itself is not usually considered a natural science. ... In mathematics and computer science, graph theory studies the properties of graphs. ... This article just presents the basic definitions. ... This article just presents the basic definitions. ... A graph is In linguistics, a letter or symbol such as an alphabetic letter, a Chinese character, or a hieroglyph. ...

Normally, the vertices of a graph by their nature are undistinguishable. (Of course, they may be distinguishable by the properties of the graph itself, e.g., by the numbers of incident edges). Some branches of graph theory require to uniquely identify vertices.

Definition

Given a mixed graph G: = (V,E,A) with V the vertices, E the edges and A the arrows of the graph, a vertex labeling is a bijective function In mathematics, a bijection, bijective function, or one-to-one correspondence is a function that is both injective (one-to-one) and surjective (onto), and therefore bijections are also called one_to_one and onto. ...

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A graph with vertex labeling is called vertex labeled.

An edge labeling is a bijective function

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A graph with edge labeling is called edge labeled.

An arrow labeling is a bijective function

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A graph with arrow labeling is called arrow labeled.

A graph with vertex, edge and arrow labeling is called completely labeled. A graph without vertex, edge or arrow labeling is called unlabeled.

See also Multigraph A multigraph is a graph with multiple edges, i. ...