| 程美群,周波.单圈图的最低及最高电阻地位[J].数学研究及应用,2022,42(5):463~475 |
| 单圈图的最低及最高电阻地位 |
| Minimum and Maximum Resistance Status of Unicyclic Graphs |
| 投稿时间：2021-07-30 修订日期：2022-02-18 |
| DOI：10.3770/j.issn:2095-2651.2022.05.003 |
| 中文关键词: 最低电阻地位 最高电阻地位 电阻距离 单圈图 极图 |
| 英文关键词:minimum resistance status maximum resistance status resistance distance unicyclic graph extremal graph |
| 基金项目:国家自然科学基金(Grant No.12071158). |
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| 中文摘要: |
| 一个连通图的一个顶点的电阻地位是这个顶点到该图的其它所有顶点的电阻距离之和. 一个连通图的最低(最高)电阻地位是这个图的所有顶点的电阻地位的最小值(最大值). 我们确定了在给定阶数的单圈图中最低(最高)电阻地位的极值和相应的极图,还讨论了单圈图的最低(最高)电阻地位与围长的关系. |
| 英文摘要: |
| The resistance status of a vertex of a connected graph is the sum of the resistance distance between this vertex and any other vertices of the graph. The minimum (maximum, resp.) resistance status of a connected graph is the minimum (maximum, resp.) resistance status of all vertices of the graph. In this paper, we determine the extremal values and corresponding extremal graphs for the minimum (maximum, resp.) resistance status over all unicyclic graphs of fixed order, and we also discuss the dependence of the minimum (maximum, resp.) resistance status on the girth of unicyclic graphs. |
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