Results 11 to 20 of about 2,886,103 (258)
VALUATIONS OF NEAR POLYGONS [PDF]
Glasgow Mathematical Journal, 2005 Ein Fast-\(2d\)-gon ist ein ungerichteter Graph ohne Schlingen vom Durchmesser \(d\), so dass zu jeder Ecke \(x\) und zu jedem maximalen clique \(M\) in \(M\) ein zu \(x\) nächster Punkt existiert. Zu jedem Fastpolygon \(\Gamma\) gehört ein partieller linearer Raum \(S\) (er wird ebenfalls Fastpolygon genannt), deren Punkte die Ecken und deren Geraden ...
B. Bruyn, P. Vandecasteele
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On m-ovoids of regular near polygons [PDF]
Designs, Codes and Cryptography, 2016 We generalise the work of Segre (Ann Mat Pura Appl 4(70):1–201, 1965), Cameron et al. (J Algebra 55(2):257–280, 1978), and Vanhove (J Algebr Comb 34(3):357–373, 2011) by showing that nontrivial m-ovoids of the dual polar spaces $$\mathsf {DQ}(2d, q)$$DQ ...
J. Bamberg, Jesse Lansdown, Melissa Lee
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Characterizations of the Suzuki tower near polygons [PDF]
Designs, Codes and Cryptography, 2016 In recent work, we constructed a new near octagon $$\mathcal {G}$$G from certain involutions of the finite simple group $$G_2(4)$$G2(4) and showed a correspondence between the Suzuki tower of finite simple groups, $$L_3(2)< U_3(3)< J_2< G_2(4) < Suz$$L3 ...
Anurag Bishnoi, B. Bruyn
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Near polygons with a nice chain of sub-near polygons
Journal of Combinatorial Theory, Series A, 2004 A near polygon is a partial linear space \({\mathcal S}=({\mathcal P},{\mathcal L})\) with the property that for every point \(p\in {\mathcal P}\) and for every line \(L\in {\mathcal L}\) there exists a unique point on \(L\) nearest to \(p\). Here distances \(d(\cdot,\cdot)\) are measured in the collinearity graph \(\Gamma\). If \(n=\text{diam}(\Gamma)\
B. Bruyn, P. Vandecasteele
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Krein conditions and near polygons
Journal of Combinatorial Theory, Series A, 1990 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. Neumaier
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European Journal of Combinatorics, 2001 A partial linear space \((P,L)\) \((P\) set points, \(L\) set of lines) is called a near polygon if the diameter of its point graph is finite and if for every pair \((p,l)\in P\times L\) there is a unique point \(q\in P\) on \(l\) nearest to \(p\) with respect to the natural distance defined on the graph.
B. Bruyn
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An inequality for regular near polygons [PDF]
European Journal of Combinatorics, 2003 Let Γ denote a near polygon distance-regular graph with diameter d ≥ 3, valency k and intersection numbers a1 > 0, c2 > 1. Let θ1 denote the second largest eigenvalue of Γ. We show θ1 ≥ k - a1 - c2/c2 - 1. We show the following (i)-(iii) are equivalent. (
Paul M. Terwilliger, Chih-wen Weng
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Near polygons and Fischer spaces [PDF]
Geometriae Dedicata, 1994 The concept of near polygon was introduced by \textit{E. Shult} and \textit{A. Yanushka} [Geom. Dedicata 9, 1-72 (1980; Zbl 0433.51008)] as a tool in the study of systems of lines in a Euclidean space. In this paper, the authors construct some infinite families of near polygons, and classify near hexagons with lines of length 3 and with quads.
A. E. Brouwer +3 more
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Homogeneous Graphs and Regular Near Polygons
Journal of Combinatorial Theory, Series B, 1994 A homogeneous graph \(\Gamma\) is defined: for every edge \(uv\), and vertex \(x\), the number of edges from \(x\) to \(\Gamma_ i(u)\cap\Gamma_ j(v)\) depends only on \(i\), \(j\) and the distances from \(x\) to \(u\) and \(v\). (\(\Gamma_ i(u)\) is the set of vertices of distance \(i\) from \(u\).) It is proven that, for distance-regular graphs in ...
K. Nomura
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The structure of near polygons with quads [PDF]
Geometriae Dedicata, 1983 We develop a structure theory for near polygons with quads. Main results are the existence of sub 2j-gons for 2jd and the nonexistence of regular sporadic 2d-gons for d4 with s>1 and t 2>1 and t 3t 2(t 2+1).
A. Brouwer, Ha Henny Wilbrink
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