On the residual closeness of graphs with cut vertices

Chengli Li (), Leyou Xu () and Bo Zhou ()
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Chengli Li: South China Normal University
Leyou Xu: South China Normal University
Bo Zhou: South China Normal University

Journal of Combinatorial Optimization, 2023, vol. 45, issue 5, No 5, 24 pages

Abstract: Abstract In designing and understanding of computer networks, how to improve network robustness or protect a network from vulnerability remains an overarching concern. The residual closeness is a measure of network vulnerability and robustness even when the removal of vertices does not disconnect the underlying graph. We determine all the graphs that minimize and maximize the residual closeness respectively over all n-vertex connected graphs with r cut vertices, where $$1\le r\le n-3$$ 1 ≤ r ≤ n - 3 .

Keywords: Residual closeness; Network vulnerability; Distances in graphs; Cut vertices (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-023-01042-5

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