A trivalent graph with 58 vertices and girth 9 |
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Authors: | N L Biggs M J Hoare |
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Institution: | Royal Holloway College, University of London, Egham, Surrey TW20 0EX, UK |
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Abstract: | The concept of a partial three-space is due to Laskar and Dunbar, and is a three-dimensional analogue of a partial geometry. Here we determine all partial three-spaces S for which the S-planes are planes of PG(n, q), for which the S-lines are all the lines contained in the S-planes, for which the S-points are all the points in the S-planes, and for which the incidence relation is that of PG(n, q). More generally, we determine all partial three-spaces S for which the S-lines are lines of PG(n,q), for which the S-points are all the points on these lines, and for which the incidence relation is that of PG(n, q). |
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