Locally GQ (3,5)-graphs and geometries with short lines

A. A. MAKHNEV

doi:10.1515/dma.1998.8.3.275

$-- An incidence system consisting of points and lines is called the -partial geometry of order (s, t) denoted by pGa(.s,0> if every line contains s+ 1 points, every point lies on / + 1 lines (lines intersect in no more than one point), and for each point a that does not belong to a line L there exist exactly lines passing through a and intersecting L. The geometry pG\ (s,t) is referred to as the generalized quadrangle, and is denoted by GQ(s,t). We prove that a connected locally G (3,5)-graph is an antipodal graph of diameter three on 160 vertices. As a consequence, we obtain a classification of homogeneous extensions of partial geometries with short lines (s < 3). This work was supported by the Russian Foundation for Basic Research, grant 96-01-00488. INTRODUCTION A geometry of rank two is an incidence system with the point set 9 and block set 58, provided that the geometry possesses no repeating blocks. Thus, the blocks can be associated with the subsets of points that are incident to them. The blocks are referred to as lines if any two blocks intersect in no more than one point. Two distinct points of$

DeepDyve - Search, Rent, Read
The easiest way for you to get scholarly articles:

Locally GQ (3,5)-graphs and geometries with short lines

MAKHNEV, A. A.

Follow Discrete Mathematics and Applications , Volume 8 (3) de Gruyter – Jan 1, 1998

Advanced Filters:

Specific Data Sources:

DeepDyve - Search, Rent, ReadThe easiest way for you to get scholarly articles:

Locally GQ (3,5)-graphs and geometries with short lines

MAKHNEV, A. A.

Follow Discrete Mathematics and Applications , Volume 8 (3) de Gruyter – Jan 1, 1998

DeepDyve - Search, Rent, Read
The easiest way for you to get scholarly articles: