On the line graph of a projective plane

This is the authors' abstract. We don't add key points for this paper.

If G is a (finite, undirected) graph, its line graph (also called the interchange graph, and the adjoint graph) is the graph G whose vertices are the edges of G, with two vertices of G adjacent if the corresponding edges of G are adjacent. Let pi be a projective plane with n 1 points on a line, and let G(pi) be the bipartite graph whose vertices are the 2(n squared n 1) points and lines of pi, with two vertices adjacent if and only if one of the vertices is a point, the other ine, and the point is on the line. The graph (G(pi)) is studied.