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一类直径为2的极大平面图的Mostar指数

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一类直径为2的极大平面图的Mostar指数 郑丽娜1, 王维凡1, 王艺桥21. 浙江师范大学数学与计算机科学学院, 金华, 321004;
2. 北京中医药大学管理学院, 北京, 100029 Mostar Index of Some Maximal Planar Graphs of Diameter Two ZHENG Lina1, WANG Weifan1, WANG Yiqiao21. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;
2. School of Management, Beijing University of Chinese Medicine, Beijing 100029, China
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摘要G的Mostar指数定义为Mo(G)=???20210102???|nu-nυ|,其中nu表示在G中到顶点u的距离比到顶点υ的距离近的顶点个数,nυ表示到顶点υ的距离比到顶点u的距离近的顶点个数.若一个图G的任两点之间的距离至多为2,且不是完全图,则称G是一个直径为2的图.已知直径为2点数至少为4的极大平面图的最小度为3或4.本文研究了直径为2且最小度为4的极大平面图的Mostar指数.具体说,若G是一个点数为n,直径为2,最小度为4的极大平面图,则(1)当n ≤ 12时,Mostar指数被完全确定;(2)当n ≥ 13时,???20210102(1)???≤Mo(G)≤2n2+16n+24,且达到上,下界的极图同时被找到.
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收稿日期: 2019-10-10
PACS:O157.5
基金资助:国家自然科学基金(12031018,11771402,11671053,12071048)以及Science and Technology Commission of Shanghai Municipality (18dz2271000)资助项目.

引用本文:
郑丽娜, 王维凡, 王艺桥. 一类直径为2的极大平面图的Mostar指数[J]. 应用数学学报, 2021, 44(1): 31-49. ZHENG Lina, WANG Weifan, WANG Yiqiao. Mostar Index of Some Maximal Planar Graphs of Diameter Two. Acta Mathematicae Applicatae Sinica, 2021, 44(1): 31-49.
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http://123.57.41.99/jweb_yysxxb/CN/ http://123.57.41.99/jweb_yysxxb/CN/Y2021/V44/I1/31


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