| Minimum and Maximum Resistance Status of Unicyclic Graphs |
| Received:July 30, 2021 Revised:February 18, 2022 |
| Key Words:
minimum resistance status maximum resistance status resistance distance unicyclic graph extremal graph
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12071158). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2022.05.003 |
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