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Journal of Combinatorial Optimization

Erschienen in:

21.10.2019

On the extremal graphs with respect to the total reciprocal edge-eccentricity

verfasst von: Lifang Zhao, Hongshuai Li, Yuping Gao

Erschienen in: Journal of Combinatorial Optimization | Ausgabe 1/2020

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The total reciprocal edge-eccentricity of a graph G is defined as \(\xi ^{ee}(G)=\sum _{u\in V_G}\frac{d_G(u)}{\varepsilon _G(u)}\), where \(d_G(u)\) is the degree of u and \(\varepsilon _G(u)\) is the eccentricity of u. In this paper, we first characterize the unique graph with the maximum total reciprocal edge-eccentricity among all graphs with a given number of cut vertices. Then we determine the k-connected bipartite graphs of order n with diameter d having the maximum total reciprocal edge-eccentricity. Finally, we identify the unique tree with the minimum total reciprocal edge-eccentricity among the n-vertex trees with given degree sequence.

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Titel: On the extremal graphs with respect to the total reciprocal edge-eccentricity
verfasst von: Lifang Zhao
Hongshuai Li
Yuping Gao
Publikationsdatum: 21.10.2019
Verlag: Springer US
Erschienen in: Journal of Combinatorial Optimization / Ausgabe 1/2020
Print ISSN: 1382-6905
Elektronische ISSN: 1573-2886
DOI: https://doi.org/10.1007/s10878-019-00458-2

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