Abstract
For a vertex x of a connected graph G=(VG,EG), the weighted reverse cover cost of x is proposed as RCπG(x)=∑y∈VGd(y)Hyx, where d(y) denotes the degree of y and Hyx denotes the hitting time for random walk starting at y to visit x. In this paper, we first obtain the sharp lower bound of RCπG(x) among all trees with order n and given diameter, and then determine the sharp upper bound of RCπG(x) among all unicyclic graphs with order n and given diameter. Furthermore, all the corresponding extremal graphs are identified.
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