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Polygon Representations of Surface Graphs

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Abstract

We use special diagrams to find some specific graphs that are embedded in some surfaces, surface graphs. Specifically, we represent each face of a surface graph G as a plane polygon with boundary vertices and edges are labelled by vertices and edges of G. Using this representation, it is possible to represent G by drawing a labelled collection of polygons. We call such a drawing a polygon representation. We use this representation to generate certain surface graphs that are tight.

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Acknowledgements

The author is grateful to James Cruickshank for suggesting the main idea of this article. Furthermore, the author would like to express his gratitude to anonymous reviewers for their valuable comments.

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  1. Department of Information Technology, Technical College of Management, Baghdad, Middle Technical University, Baghdad, Iraq

    Qays R. Shakir

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Correspondence to Qays R. Shakir.

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Shakir, Q.R. Polygon Representations of Surface Graphs. Vietnam J. Math. (2023). https://doi.org/10.1007/s10013-023-00620-8

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