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  4. A property of a particular generalized Petersen unit-distance graph

A property of a particular generalized Petersen unit-distance graph

MMC.
2025;
Volume 12, Number 2
: pp. 461–467
https://doi.org/10.23939/mmc2025.02.461
Received: December 20, 2024
Revised: May 11, 2025
Accepted: May 17, 2025

Kaenthong N., Thongnork P., Thongroek P., Siriwong P.  A property of a particular generalized Petersen unit-distance graph.  Mathematical Modeling and Computing. Vol. 12, No. 2, pp. 461–460 (2025)  

Authors:
  1. N. Kaenthong
  2. P. Thongnork
  3. P. Thongroek
  4. P. Siriwong
1
Mathematics, Faculty of Education and Faculty of Science and Digital Innovation, Thaksin University
2
Mathematics, Faculty of Education and Faculty of Science and Digital Innovation, Thaksin University
3
Mathematics, Faculty of Education and Faculty of Science and Digital Innovation, Thaksin University
4
Mathematics and Data Management Program, Faculty of Science and Digital Innovation, Thaksin University

A generalized Petersen graph is a graph with $2n$ vertices, where each vertex has degree 3 and there are $3n$ edges.  A unit-distance graph is a graph with every edge of 1 unit  length.  We study the geometric transformation of a generalized Petersen graph into a generalized Petersen unit-distance graph and the rotation angles of the $n$-pointed star of the generalized Petersen unit-distance graph.  Then, we obtain the properties of the generalized Petersen unit-distance graph and the rotation angles of the $n$-pointed star of the generalized Petersen unit-distance graph by using geometric transformations, trigonometric functions, and the rule of sine and cosine, along with similar polygons.

generalized Petersen graph
unit-distance
rotation angles
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