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A property of a particular generalized Petersen unit-distance graph
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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.
Lviv Polytechnic National University
Title: A property of a particular generalized Petersen unit-distance graph
Description:
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.
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