2024/07/15 by Rigoberto Flórez, Flórez, Rigoberto, Thomas Zasĺavsky +1
Computer Science · Engineering · #Graph Labeling and Dimension Problems #graph theory and CDMA systems #Computational Geometry and Mesh Generation
paper · pdf · doi:10.48550/arxiv.2407.11285
A projective rectangle is like a projective plane that may have different lengths in two directions. We develop properties of the graph of lines, in which adjacency means having a common point, especially its strong regularity and clique structure. The main construction of projective rectangles, stated in a previous paper, gives rectangles whose graph of lines is a known strongly regular bilinear forms graph. That fact leads to a proof that the main construction does produce projective rectangles, and also gives a new representation of bilinear forms graphs. We conclude by mentioning a few simple graph properties, such as the chromatic number, which is not known, and a partial geometry obtained from the graph.