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Super Connectivity of Erdős-Rényi Graphs

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  • Yilun Shang

    (Department of Computer and Information Sciences, Faculty of Engineering and Environment, Northumbria University, Newcastle NE1 8ST, UK)

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.

Suggested Citation

  • Yilun Shang, 2019. "Super Connectivity of Erdős-Rényi Graphs," Mathematics, MDPI, vol. 7(3), pages 1-5, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:267-:d:214257
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    References listed on IDEAS

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    1. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
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    Cited by:

    1. Zhifeng Dai & Huan Zhu, 2020. "A Modified Hestenes-Stiefel-Type Derivative-Free Method for Large-Scale Nonlinear Monotone Equations," Mathematics, MDPI, vol. 8(2), pages 1-14, January.

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