Bicyclic graphs with extremal cover cost

Jian Lu, Xiang-Feng Pan and Huiqing Liu

Applied Mathematics and Computation, 2021, vol. 405, issue C

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.

Keywords: Bicyclic graph; Expected hitting time; Cover cost (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:405:y:2021:i:c:s0096300321003258

DOI: 10.1016/j.amc.2021.126235

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