A property of a particular generalized Petersen unit-distance graph

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 an...

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Published inMathematical Modeling and Computing Vol. 12; no. 2; pp. 461 - 467
Main Authors Kaenthong, N., Thongnork, P., Thongroek, P., Siriwong, P.
Format Journal Article
LanguageEnglish
Published 2025
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Abstract 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.
AbstractList 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.
Author Siriwong, P.
Kaenthong, N.
Thongroek, P.
Thongnork, P.
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Cites_doi 10.1007/BF01864150
10.1016/j.disc.2007.04.050
10.1016/j.disc.2009.11.035
10.37236/269
10.4134/JKMS.2012.49.3.475
10.1017/mag.2019.74
10.1006/jctb.1998.1819
10.1016/j.disc.2022.113106
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CorporateAuthor Mathematics and Data Management Program, Faculty of Science and Digital Innovation, Thaksin University
Mathematics, Faculty of Education and Faculty of Science and Digital Innovation, Thaksin University
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