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- W2953124293 abstract "Let $G=(V_G, E_G)$ be a simple connected graph. The eccentric distance sum of $G$ is defined as $xi^{d}(G) = sum_{vin V_G}varepsilon_{G}(v)D_{G}(v)$, where $varepsilon_G(v)$ is the eccentricity of the vertex $v$ and $D_G(v) = sum_{uin V_G}d_G(u,v)$ is the sum of all distances from the vertex $v$. In this paper the tree among $n$-vertex trees with domination number $gamma$ having the minimal eccentric distance sum is determined and the tree among $n$-vertex trees with domination number $gamma$ satisfying $n = kgamma$ having the maximal eccentric distance sum is identified, respectively, for $k=2,3,frac{n}{3},frac{n}{2}$. Sharp upper and lower bounds on the eccentric distance sums among the $n$-vertex trees with $k$ leaves are determined. Finally, the trees among the $n$-vertex trees with a given bipartition having the minimal, second minimal and third minimal eccentric distance sums are determined, respectively." @default.
- W2953124293 created "2019-06-27" @default.
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- W2953124293 date "2012-06-30" @default.
- W2953124293 modified "2023-10-17" @default.
- W2953124293 title "Extremal values on the eccentric distance sum of trees" @default.
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- W2953124293 doi "https://doi.org/10.48550/arxiv.1207.0083" @default.
- W2953124293 hasPublicationYear "2012" @default.
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