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Chapter 4 introduces the operation of diagonal flip, by which one can transform a pair of maximal planar graphs with the same order into each other. In this chapter, we fucus on the methods of constructing a maximal planar graph from another one with different order; that is, start with a small order maximal planar graph, e.g., tetrahedron, octahedron or icosahedron, one can obtain a maximal planar graph with a give order by a serious of operations. This can be represented as a generating system, denoted by \(&lt;G_ _varPhi=""&gt;\) , where G is the starting graph and \(\varPhi \) is a set of operations, called operators. The generating systems of constructing maximal planar graphs, in particular, those of minimum degree 5 or of even number order, will be argued in detail in the following.</G_>

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Construction of Maximal Planar Graphs with the Different Order

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  • 出版模式：

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  • 发表日期：

    2025年

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  • Jin Xu

摘要

Chapter 4 introduces the operation of diagonal flip, by which one can transform a pair of maximal planar graphs with the same order into each other. In this chapter, we fucus on the methods of constructing a maximal planar graph from another one with different order; that is, start with a small order maximal planar graph, e.g., tetrahedron, octahedron or icosahedron, one can obtain a maximal planar graph with a give order by a serious of operations. This can be represented as a generating system, denoted by \(<G_ _varPhi="">\) , where G is the starting graph and \(\varPhi \) is a set of operations, called operators. The generating systems of constructing maximal planar graphs, in particular, those of minimum degree 5 or of even number order, will be argued in detail in the following.