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Bicyclic graphs with extremal cover cost

Author

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  • Lu, Jian
  • Pan, Xiang-Feng
  • Liu, Huiqing

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.

Suggested Citation

  • Lu, Jian & Pan, Xiang-Feng & Liu, Huiqing, 2021. "Bicyclic graphs with extremal cover cost," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    • Handle: RePEc:eee:apmaco:v:405:y:2021:i:c:s0096300321003258
    DOI: 10.1016/j.amc.2021.126235
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    Cited by:

    1. Lv, Yan & Chen, Zhouyang & Wu, Tingzeng & Zhang, Peng-Li, 2024. "On the weighted reverse cover cost of trees and unicyclic graphs with given diameter," Applied Mathematics and Computation, Elsevier, vol. 473(C).

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