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

Lifang Zhao (), Hongshuai Li () and Yuping Gao ()
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Lifang Zhao: Lanzhou University
Hongshuai Li: Zhongshan Overseas Chinese Secondary School
Yuping Gao: Lanzhou University

Journal of Combinatorial Optimization, 2020, vol. 39, issue 1, No 8, 115-137

Abstract: Abstract The total reciprocal edge-eccentricity of a graph G is defined as $$\xi ^{ee}(G)=\sum _{u\in V_G}\frac{d_G(u)}{\varepsilon _G(u)}$$ξee(G)=∑u∈VGdG(u)εG(u), where $$d_G(u)$$dG(u) is the degree of u and $$\varepsilon _G(u)$$εG(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.

Keywords: Total reciprocal edge-eccentricity; Cut vertex; Eccentricity; Degree sequence; 05C69; 05C05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10878-019-00458-2

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