Motivated by the connection with the genus of the corresponding link and its application on DNA polyhedral links, in this paper, we introduce a parameter s_max(G), which is the maximum number of circles of states of the link diagram D(G) corresponding to a plane (positive) graph G. We show that s_max(G) does not depend on the embedding of G and if G is a 4-edge-connected plane graph then s_max(G) is equal to the number of faces of G, which cover the results of S. Y. Liu and H. P. Zhang as special cases.

中文翻译：

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平面图的最大状态的圈数及其应用

出于与相应链接属的联系及其在DNA多面链接中的应用的动机，在本文中，我们引入了一个参数s _max（G），它是链接图D（G）的最大状态圈数。对应于平面图（正图）G。我们证明s _max（G）不依赖于G的嵌入，并且如果G是4边连接的平面图，则s _max（G）等于G的面数，其中以特殊情况涵盖了刘SY和HP Zhang的结果。