line graph

Noun

 * 1) A graph in which a series of connected straight lines connect points, each of which represents the value of a particular variable as a function of another variable.
 * 2)  A graph L(G) which is derived from a given non-oriented graph G such that the vertices of L(G) represent edges of G and so that a clique in L(G) represents a common end-vertex shared by a set of represented edges. (A  in G transforms into a clique in L(G).)
 * 3) A graph which is the line graph (in the above sense) of some other graph.
 * Suppose that a graph G has vertices A, B, C, and D such that A is adjacent to each of B, C, and D, but {B, C, D} is an independent set. Then G cannot be a line graph.
 * Suppose that a graph G has vertices A, B, C, and D such that A is adjacent to each of B, C, and D, but {B, C, D} is an independent set. Then G cannot be a line graph.

Translations

 * Chinese:
 * Mandarin: 折線圖
 * German:
 * Portuguese: gráfico de linha


 * Chinese:
 * Mandarin:
 * French: line graph, graphe adjoint
 * German: Kantengraph
 * Spanish: grafo línea, grafo de línea, grafo lineal, grafo representativo