Journal
JOURNAL OF COMBINATORIAL OPTIMIZATION
Volume 39, Issue 1, Pages 115-137Publisher
SPRINGER
DOI: 10.1007/s10878-019-00458-2
Keywords
Total reciprocal edge-eccentricity; Cut vertex; Eccentricity; Degree sequence
Funding
- Fundamental Research Funds for the Central Universities [lzujbky-2017-28]
- Yuping Gao: NSFC [11901263]
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The total reciprocal edge-eccentricity of a graph G is defined as xi(ee)(G) = Sigma(u is an element of VG) d(G)(u)/epsilon(G)(u), where d(G)(u) is the degree of u and epsilon(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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