On the weighted reverse cover cost of trees and unicyclic graphs with given diameter

Yan Lv, Zhouyang Chen, Tingzeng Wu and Peng-Li Zhang

Applied Mathematics and Computation, 2024, vol. 473, issue C

Abstract: For a vertex x of a connected graph G=(VG,EG), the weighted reverse cover cost of x is proposed as RCπG(x)=∑y∈VGd(y)Hyx, where d(y) denotes the degree of y and Hyx denotes the hitting time for random walk starting at y to visit x. In this paper, we first obtain the sharp lower bound of RCπG(x) among all trees with order n and given diameter, and then determine the sharp upper bound of RCπG(x) among all unicyclic graphs with order n and given diameter. Furthermore, all the corresponding extremal graphs are identified.

Keywords: Trees; Unicyclic graphs; Weighted reverse cover cost; Diameter (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:473:y:2024:i:c:s0096300324001462

DOI: 10.1016/j.amc.2024.128674

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