Linked from

The 13 pages that link to Line graph, each with the reason it gives.

• Bipartite graphRelated: This transformation can turn a bipartite graph into a non-bipartite graph.

• Incidence matrixRelated: It captures edge adjacency, a relation that can be derived from incidence information.

• Vertex (graph theory)Compared with: It reverses the usual emphasis by treating connections as vertices.

• MultigraphRelated: Distinct parallel edges become distinct adjacent vertices in the line graph.

• Edge coloringRelated: Edge coloring becomes ordinary vertex coloring on the corresponding line graph.

• Bipartite matchingRelated: A matching becomes an independent set after translating edges into vertices.

• Regular graphRelated: For an r-regular graph, its line graph is 2(r−1)-regular.

• Edge coverRelated: It translates edge relationships into vertex relationships, helping distinguish edge-based covering notions.

• Erdős–Faber–Lovász conjectureRelated: Recasting each constituent graph as a hyperedge turns the coloring question into coloring a line graph.

• Hosoya indexRelated: Matchings in the original graph correspond to cliques in its line graph.

• Intersection graphBroader topic: It is an intersection graph of the original graph’s edge-endpoint sets.

• Fleischner's theoremRelated: Graph transformations such as line graphs provide neighboring settings for Hamiltonicity theorems.

• List coloring conjectureRelated: Edge coloring becomes vertex coloring on this associated graph.