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- W4379933229 abstract "Given a connected graph $G$, Kemeny's constant $mathcal{K}({G})$ measures the average travel time for a random walk to reach a randomly selected vertex. It is known that when an edge is added to $G$, the value of Kemeny's constant may either decrease, increase, or stay the same. In this paper, we present a quantitative analysis of this behaviour when the initial graph is a tree with $n$ vertices. We prove that when an edge is added into a tree on $n$ vertices, the maximum possible increase in Kemeny's constant is roughly $frac{2}{3}n,$ while the maximum possible decrease is roughly $frac{3}{16}n^2$. We also identify the trees, and the edges to be added, that correspond to the maximum increase and maximum decrease. Throughout, both matrix theoretic and graph theoretic techniques are employed." @default.
- W4379933229 created "2023-06-09" @default.
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- W4379933229 date "2023-06-06" @default.
- W4379933229 modified "2023-09-26" @default.
- W4379933229 title "Edge Addition and the Change in Kemeny's Constant" @default.
- W4379933229 doi "https://doi.org/10.48550/arxiv.2306.04005" @default.
- W4379933229 hasPublicationYear "2023" @default.
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