The Number of Circles of a Maximum State of a Plane Graph with Applications

• 作者: Xian-an JIN Jun GE Xiao-Sheng CHENG Yu-qing LIN
• 来源期刊: 应用数学学报（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 409-420
• 页数: 12页
• 语种: 英文

摘要

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 Smax(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 Smax(G) does not depend on the embedding of G and if G is a 4-edge-connected plane graph then Smax(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.