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Line chart showing the population of the town of Pushkin, Saint Petersburg from 1800 to 2010, measured at various intervals. A line chart or line graph, also known as curve chart, [1] is a type of chart that displays information as a series of data points called 'markers' connected by straight line segments. [2]
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G).
Vertex coloring is often used to introduce graph coloring problems, since other coloring problems can be transformed into a vertex coloring instance. For example, an edge coloring of a graph is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring ...
Pages in category "Graph coloring" The following 82 pages are in this category, out of 82 total. ... Conflict-free coloring; Critical graph; D. De Bruijn–Erdős ...
An edge coloring of is called a -rainbow coloring if for every set of vertices of , there is a rainbow tree in containing the vertices of . The k {\displaystyle k} -rainbow index rx k ( G ) {\displaystyle {\text{rx}}_{k}(G)} of G {\displaystyle G} is the minimum number of colors needed in a k {\displaystyle k} -rainbow coloring of G ...
Specifically, a Hamiltonian coloring's nodes have the property that the detour distance plus the difference in colors is greater than or equal to one less than n, the number of nodes in the graph. If the graph G is a path, then any Hamiltonian coloring is also an antipodal coloring, which is the inspiration for the definition of Hamiltonian ...
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Exact coloring of the complete graph K 6. Every n-vertex complete graph K n has an exact coloring with n colors, obtained by giving each vertex a distinct color. Every graph with an n-color exact coloring may be obtained as a detachment of a complete graph, a graph obtained from the complete graph by splitting each vertex into an independent set and reconnecting each edge incident to the ...