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arXiv · 2407.11285

Projective Rectangles: The Graph of Lines

Rigoberto Flórez·Thomas Zaslavsky
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Abstract

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.

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Rigoberto Flórez, Thomas Zaslavsky. 2024-07-15. Projective Rectangles: The Graph of Lines. https://arxiv.org/abs/2407.11285

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