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Line graph

A line graph (also called an adjoint, conjugate, covering, derivative, derived, edge, edge-to-vertex dual, interchange, representative, or -obrazom graph) of a simple graph is obtained by associating a vertex with each edge of the graph and connecting two vertices with an edge iff the corresponding edges of have a vertex in common (Gross and Yellen 2006, p. 20).The line graph of a directed graph is the directed graph whose vertex set corresponds to the arc set of and having an arc directed from an edge to an edge if in , the head of meets the tail of (Gross and Yellen 2006, p. 265).Line graphs are implemented in the Wolfram Language as LineGraph[g]. Precomputed line graph identifications of many named graphs can be obtained in the Wolfram Language using GraphData[graph, "LineGraphName"].The numbers of simple line graphs on , 2, ... vertices are 1, 2, 4, 10, 24, 63, 166, 471, 1408, ... (OEIS A132220), and the numbers of connected..

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