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Mathematics 2019, 7(3), 267; https://doi.org/10.3390/math7030267

Super Connectivity of Erdős-Rényi Graphs

Department of Computer and Information Sciences, Faculty of Engineering and Environment, Northumbria University, Newcastle NE1 8ST, UK
Received: 9 February 2019 / Revised: 8 March 2019 / Accepted: 12 March 2019 / Published: 15 March 2019
(This article belongs to the Section Network Science)
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Abstract

The super connectivity κ ( G ) of a graph G is the minimum cardinality of vertices, if any, whose deletion results in a disconnected graph that contains no isolated vertex. G is said to be r-super connected if κ ( G ) r . In this note, we establish some asymptotic almost sure results on r-super connectedness for classical Erdős–Rényi random graphs as the number of nodes tends to infinity. The known results for r-connectedness are extended to r-super connectedness by pairing off vertices and estimating the probability of disconnecting the graph that one gets by identifying the two vertices of each pair. View Full-Text
Keywords: super connectivity; random graph; interconnection network super connectivity; random graph; interconnection network
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Shang, Y. Super Connectivity of Erdős-Rényi Graphs. Mathematics 2019, 7, 267.

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