
On Distance in Some Finite Planes and Graphs Arising from Those Planes
Author(s) -
İsa Doğan,
Ati̇lla Akpinar
Publication year - 2021
Publication title -
journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.252
H-Index - 13
eISSN - 2314-4785
pISSN - 2314-4629
DOI - 10.1155/2021/6668682
Subject(s) - mathematics , hyperbola , projective plane , affine transformation , combinatorics , affine geometry , euclidean geometry , fano plane , affine plane (incidence geometry) , finite geometry , ellipse , projective space , discrete mathematics , projective test , affine space , pure mathematics , plane (geometry) , geometry , correlation
In this paper, affine and projective graphs are obtained from affine and projective planes of order p r by accepting a line as a path. Some properties of these affine and projective graphs are investigated. Moreover, a definition of distance is given in the affine and projective planes of order p r and, with the help of this distance definition, the point or points having the most advantageous (central) position in the corresponding graphs are determined, with some examples being given. In addition, the concepts of a circle, ellipse, hyperbola, and parabola, which are well known for the Euclidean plane, are carried over to these finite planes. Finally, the roles of finite affine and projective Klingenberg planes in all the results obtained are considered and their equivalences in graph applications are discussed.