Abstract
The expected hitting time Hxy is the expected number of steps it takes for a random walk that starts at x to reach y. For a vertex x of G, the cover cost of x, denoted by CCG(x), is defined as the sum of the expected hitting time for a random walk starting at x to visit all vertices of G. In this paper, we first reveal a close connection between the cover cost and some related graph invariants of bicyclic graphs, and then present sharp bounds of CCG(x) among all bicyclic graphs of order n and characterize the corresponding extremal graphs.
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