Quoting Michael Reid <reid@math.ucf.edu>:
Is there a name for the operation which takes one graph to another, such that the points of the new graph are the edges of the original graph, and there is an edge between two such points if their originating edges shared a point? I.e., each edge becomes a point, and a point with valence n becomes C(n,2) edges.
i believe the resulting graph is called the _line_graph_ of the original graph. i do not know if there's a specific term for the *operation* involved.
I think the term "line graph" comes from the 1930's when Hassler Whitney wote about them. Another term is "dual graph," and one of Whitney's interests was in finding the conditions under which a given graph was itself a dual. It has to do with whether the connection matrix has an R-C (row matrix times column matrix) factorization and looks much like the L-R (left triangular, right triangular) factorization used in diagonalizing matrices. There are dual chains and dual towers; maybe the operation could be called "dualization," but I can't think of any familiar phrase. - hvm ------------------------------------------------- www.correo.unam.mx UNAMonos Comunicándonos