On the resistance diameter of hypercubes

Abstract The resistance distance among two vertices in some resistor networks has been widely considered by many physicists and mathematicians. The resistance diameter of a graph is defined by the maximum resistance distance among all pairs of vertices in the graph. The study of resistance diameter was initiated here. It seems to be possible that the resistance diameter of a graph could play a significant role in analyzing the efficiency of the interconnection networks for wave- or fluid-like communication. In order to improve the efficiency of wave- or fluid-like communication, we need to minimize the resistance diameter of graphs. The class of hypercubes is most common, multipurpose and efficient topological structure class of interconnection networks. Hypercube networks satisfy most requirements for the basic principles of network design. The main result of this paper is to give a combinatorial formula for the resistance diameter of hypercubes. In addition, the minimum resistance distance among all pairs of vertices in hypercubes is also obtained. These two results are deduced via the electrical network approach and the hitting time of random walks, respectively.