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Concept
Graph labeling
Summary
In the mathematical discipline of graph theory, a graph labelling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph.
Formally, given a graph G = (V, E), a vertex labelling is a function of V to a set of labels; a graph with such a function defined is called a vertex-labeled graph. Likewise, an edge labelling is a function of E to a set of labels. In this case, the graph is called an edge-labeled graph.
When the edge labels are members of an ordered set (e.g., the real numbers), it may be called a weighted graph.
When used without qualification, the term labeled graph generally refers to a vertex-labeled graph with all labels distinct. Such a graph may equivalently be labeled by the consecutive integers { 1, …, } , where is the number of vertices in the graph. For many applications, the edges or vertices are given labels that are meaningful in the associated domain. For example, the e
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