Ref Book : Graph Theory and Its Application by Jonathan L. Gross & Jay Yellen A line graph L(G) (also called adjoint, conjugate, covering, derivative, derived, edge, edge-to-vertex dual, interchange, representative, or theta-obrazom graph) of a simple graph G is obtained by associating a vertex with each edge of the graph and connecting two vertices with an edge iff the corresponding edges of G have a vertex in common.