Minimum and maximum resistance status of graphs

英文关键词:minimum resistance status, maximum resistance status, resistance distance unicyclic graph, extremal graph

中文摘要:

      

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, respectively) resistance status of a connected graph is the minimum (maximum, respectively) resistance status of all vertices of the graph. In this paper, we determine the extremal values and extremal graphs for minimum (maximum, respectively) resistance status over all unicyclic graphs of fixed order, and we also discuss the dependence of minimum (maximum, respectively) resistance status on the girth of unicyclic graphs.