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Abstract
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In this talk, a close relation between hitting times of the simple random walk on a graph, the Kirchhoff index, the resistance-centrality, and related invariants of graphs is displayed. Combining graph transformations and some other techniques, sharp upper and lower bounds on the cover cost (resp. reverse cover cost), the multiplicative degree-Kirchhoff index, the number of spanning trees of graphs are determined. All the corresponding extremal graphs are identified.
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