On distance in some finite planes and graphs arising from those planes
type: Item
instance of: scholarly article
title: On distance in some finite planes and graphs arising from those planes
zbMATH Open document ID: 1477.05054
DOI: 10.1155/2021/6668682
author: Yanyan Li
published in: Journal of Mathematics
publication date: 2021-06-22T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 51C05
zbMATH DE Number: 7362014
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6668682
OpenAlex ID: W3123173337
cites work: Galois theory.
cites work: A computer search for finite projective planes of order 9
cites work: The Search for a Finite Projective Plane of Order 10
cites work: Q5657309
cites work: Q4484908
cites work: Q5683869
cites work: Q3974205
cites work: A textbook of graph theory
cites work: Q3097395
cites work: Q4873725
cites work: Projectivities in Moufang-Klingenberg planes
cites work: 4-transitivity and cross-ratio in Moufang-Klingenberg planes over rings of plural numbers
cites work: Octonion Planes Over Local Rings
cites work: Finite Hjelmslev planes
cites work: Finite Klingenberg planes
cites work: Q3743960
cites work: Q4885576
cites work: On non-commutative rank and tensor rank
cites work: Q3797777
description: scientific article; zbMATH DE number 7362014