Formal Definition
Given a graph G, its line graph L(G) is a graph such that
- each vertex of L(G) represents an edge of G; and
- two vertices of L(G) are adjacent if and only if their corresponding edges share a common endpoint ("are adjacent") in G.
That is, it is the intersection graph of the edges of G, representing each edge by the set of its two endpoints.
Read more about this topic: Line Graph
Famous quotes containing the words formal and/or definition:
“The conviction that the best way to prepare children for a harsh, rapidly changing world is to introduce formal instruction at an early age is wrong. There is simply no evidence to support it, and considerable evidence against it. Starting children early academically has not worked in the past and is not working now.”
—David Elkind (20th century)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)