Elsevier

Discrete Mathematics

Volume 342, Issue 1, January 2019, Pages 78-95
Discrete Mathematics

Further results on the expected hitting time, the cover cost and the related invariants of graphs

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Abstract

A close relation between hitting times of the simple random walk on a graph, the Kirchhoff index, the resistance-centrality, and related invariants of unicyclic graphs is displayed. Combining graph transformations and some other techniques, sharp upper and lower bounds on the cover cost (resp. reverse cover cost) of a vertex in an n-vertex unicyclic graph are determined. All the corresponding extremal graphs are identified.

Keywords

Random walk
Hitting time
Kirchhoff index
Cover cost
Reverse cover cost

Cited by (0)

J. H. acknowledges the excellent doctoral dissertation cultivation grant from Central China Normal University (Grant Nos. 2017YBZZ105), S. L. acknowledges the financial support from the National Natural Science Foundation of China (grant nos. 11671164, 11771172, 11271149) and Z. X. acknowledges the financial support from the National Natural Science Foundation of China (grant no. 61773020).