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Sufficient Conditions for Graphs to Be k-Connected, Maximally Connected, and Super-Connected

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  • Zhen-Mu Hong
  • Zheng-Jiang Xia
  • Fuyuan Chen
  • Lutz Volkmann
  • M. Irfan Uddin

Abstract

Let G be a connected graph with minimum degree δG and vertex-connectivity κG. The graph G is k-connected if κG≥k, maximally connected if κG=δG, and super-connected if every minimum vertex-cut isolates a vertex of minimum degree. In this paper, we present sufficient conditions for a graph with given minimum degree to be k-connected, maximally connected, or super-connected in terms of the number of edges, the spectral radius of the graph, and its complement, respectively. Analogous results for triangle-free graphs with given minimum degree to be k-connected, maximally connected, or super-connected are also presented.

Suggested Citation

  • Zhen-Mu Hong & Zheng-Jiang Xia & Fuyuan Chen & Lutz Volkmann & M. Irfan Uddin, 2021. "Sufficient Conditions for Graphs to Be k-Connected, Maximally Connected, and Super-Connected," Complexity, Hindawi, vol. 2021, pages 1-11, February.
    • Handle: RePEc:hin:complx:5588146
    DOI: 10.1155/2021/5588146
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    Cited by:

    1. Guifu Su & Shuai Wang & Junfeng Du & Mingjing Gao & Kinkar Chandra Das & Yilun Shang, 2022. "Sufficient Conditions for a Graph to Be ℓ -Connected, ℓ -Deficient, ℓ -Hamiltonian and ℓ − -Independent in Terms of the Forgotten Topological Index," Mathematics, MDPI, vol. 10(11), pages 1-11, May.

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