Quadrance polygons, association schemes and strongly regular graphs
| dc.creator | Vinh, Le Anh | |
| dc.date | 2005-09-26 | |
| dc.date.accessioned | 2026-07-07T06:19:11Z | |
| dc.date.available | 2026-07-07T06:19:11Z | |
| dc.description | Quadrance between two points A_1 = [x_1,y_1] and A_2 = [x_2,y_2] is the number Q (A_1, A_2) := (x_2 - x_1)^2 + (y_2 - y_1)^2. In this paper, we present some interesting results arise from this notation. In Section 1, we will study geometry over finite fields under quadrance notations. The main purpose of Section 1 is to answer the question, for which a_1,...,a_n, we have a polygon A_1...A_n such that Q(A_i,A_{i+1})=a_i for i = 1,...,n. In Section 2, using tools developed in Section 1, we define a family of association schemes over finite field space F_q x F_q where q is a prime power. These schemes give rise to a graph V_q with vertices the points of F_q^2, and where (X,Y) is an edge of V_q if and only if Q(X,Y) is a nonzero square number in F_q. In Section 3, we will show that V_q is a strongly regular graph and propose a conjecture about the maximal clique of V_q. | |
| dc.description | 15 pages, submitted | |
| dc.identifier | https://arxiv.org/abs/math/0509598 | |
| dc.identifier | http://arxiv.org/abs/math/0509598 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94987 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.title | Quadrance polygons, association schemes and strongly regular graphs | |
| dc.type | text |