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• W3136758443 abstract "The relation between the Wiener index W(G) and the eccentricity $$varepsilon (G)$$ of a graph G is studied. Lower and upper bounds on W(G) in terms of $$varepsilon (G)$$ are proved and extremal graphs characterized. A Nordhaus–Gaddum type result on W(G) involving $$varepsilon (G)$$ is given. A sharp upper bound on the Wiener index of a tree in terms of its eccentricity is proved. It is shown that in the class of trees of the same order, the difference $$W(T) - varepsilon (T)$$ is minimized on caterpillars. An exact formula for $$W(T) - varepsilon (T)$$ in terms of the radius of a tree T is obtained. A lower bound on the eccentricity of a tree in terms of its radius is also given. Two conjectures are proposed. The first asserts that the difference $$W(G) - varepsilon (G)$$ does not increase after contracting an edge of G. The second conjecture asserts that the difference between the Wiener index of a graph and its eccentricity is largest on paths." @default.
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• W3136758443 date "2021-03-17" @default.
• W3136758443 modified "2023-10-10" @default.
• W3136758443 title "On the relation between Wiener index and eccentricity of a graph" @default.
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• W3136758443 doi "https://doi.org/10.1007/s10878-021-00724-2" @default.
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