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  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12071158).
Author NameAffiliation
Meiqun CHENG School of Mathematical Sciences, South China Normal University, Guangdong 510631, P. R. China 
Bo ZHOU School of Mathematical Sciences, South China Normal University, Guangdong 510631, P. R. China 
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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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