ON THE LINE GRAPH OF A PROJECTIVE PLANE
IBM THOMAS J WATSON RESEARCH CENTER YORKTOWN HEIGHTS NY
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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 Gpi be the bipartite graph whose vertices are the 2n 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 Gpi is studied.
- Theoretical Mathematics