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In the mathematical discipline of graph theory, a graph labeling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. [ 1 ] Formally, given a graph G = ( V , E ) , a vertex labeling is a function of V to a set of labels; a graph with such a function defined is called a vertex-labeled graph .
Matched with attributed graphs, these labels correspond to attributes comprising only a key, taken from a countable set (typically a character string, or an integer) Colored graphs, as used in classical graph coloring problems, are special cases of labeled graphs, whose labels are defined on a finite set of keys, matched to colors.
GSS (Graph Style Sheets) in mathematics and computing, is an RDF (Resource Description Framework) vocabulary for representation of data in a model of labeled directed graph. [1] Using it will make a relatively complex data resource modeled in RDF , much easier to understand by declaring simple styling and visibility instructions to be applied ...
Label the two edges in the following way: the edge (v 1, v 2) is labeled 1 and (v 2, v 3) labeled 2. The induced labelings on v 1, v 2, and v 3 are then 1, 0, and 2 respectively. This is an edge-graceful labeling and so P 3 is edge-graceful. Similarly, one can check that P 4 is not edge-graceful.
A graceful labeling. Vertex labels are in black, edge labels in red.. In graph theory, a graceful labeling of a graph with m edges is a labeling of its vertices with some subset of the integers from 0 to m inclusive, such that no two vertices share a label, and each edge is uniquely identified by the absolute difference between its endpoints, such that this magnitude lies between 1 and m ...
The R programming language can be used for creating Wikipedia graphs. The Google Chart API allows a variety of graphs to be created. Livegap Charts creates line, bar, spider, polar-area and pie charts, and can export them as images without needing to download any tools. Veusz is a free scientific graphing tool that can produce 2D and 3D plots ...
A labeled tree is a tree in which each vertex is given a unique label. The vertices of a labeled tree on n vertices (for nonnegative integers n ) are typically given the labels 1, 2, …, n . A recursive tree is a labeled rooted tree where the vertex labels respect the tree order (i.e., if u < v for two vertices u and v , then the label of u is ...
Distinguishing coloring of a 4-hypercube graphIn graph theory, a distinguishing coloring or distinguishing labeling of a graph is an assignment of colors or labels to the vertices of the graph that destroys all of the nontrivial symmetries of the graph.