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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).
The dual graph for a Voronoi diagram (in the case of a Euclidean space with point sites) corresponds to the Delaunay triangulation for the same set of points. The closest pair of points corresponds to two adjacent cells in the Voronoi diagram. Assume the setting is the Euclidean plane and a discrete set of points is given.
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]
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 many edges and not the exact layout. In practice, it is often difficult to decide if two drawings represent the same ...
In the mathematical field of graph theory, Fáry's theorem states that any simple, planar graph can be drawn without crossings so that its edges are straight line segments. That is, the ability to draw graph edges as curves instead of as straight line segments does not allow a larger class of graphs to be drawn.
quasi-line graph A quasi-line graph or locally co-bipartite graph is a graph in which the open neighborhood of every vertex can be partitioned into two cliques. These graphs are always claw-free and they include as a special case the line graphs. They are used in the structure theory of claw-free graphs. quasi-random graph sequence
Graph drawing; Graph homomorphism; Graph labeling. Graceful labeling; Graph partition; Graph pebbling; Graph property; Graph reduction; Graph-structured stack; Graphical model. Bayesian network; D-separation; Markov random field; Tree decomposition (Junction tree) and treewidth; Graph triangulation (see also Chordal graph) Perfect order; Hidden ...
The line graph construction of the three smallest binary De Bruijn graphs is depicted below. As can be seen in the illustration, each vertex of the n -dimensional De Bruijn graph corresponds to an edge of the ( n – 1) -dimensional De Bruijn graph, and each edge in the n -dimensional De Bruijn graph corresponds to a two-edge path in the ( n ...