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Maximally edge-connected graphs and Zeroth-order general Randić index for $$\alpha \le -1$$ α ≤ - 1

Author

Listed:
  • Guifu Su

    (Beijing Institute of Technology
    University of Georgia)

  • Liming Xiong

    (Beijing Institute of Technology)

  • Xiaofeng Su

    (Shanghai Maritime University)

  • Guojun Li

    (University of Georgia)

Abstract

Let $$G$$ G be a connected graph with order $$n,$$ n , minimum degree $$\delta =\delta (G)$$ δ = δ ( G ) and edge-connectivity $$\lambda =\lambda (G).$$ λ = λ ( G ) . A graph $$G$$ G is maximally edge-connected if $$\lambda =\delta .$$ λ = δ . In this paper, we present two sufficient conditions for graphs to be maximally edge-connected, which generalize two results recently proved by P. Dankelmann, A. Hellwig and L. Volkmann. The extremal graphs are also characterized.

Suggested Citation

  • Guifu Su & Liming Xiong & Xiaofeng Su & Guojun Li, 2016. "Maximally edge-connected graphs and Zeroth-order general Randić index for $$\alpha \le -1$$ α ≤ - 1," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 182-195, January.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:1:d:10.1007_s10878-014-9728-y
    DOI: 10.1007/s10878-014-9728-y
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    Cited by:

    1. Muhammad Kamran Jamil & Ioan Tomescu & Muhammad Imran & Aisha Javed, 2020. "Some Bounds on Zeroth-Order General Randić Index," Mathematics, MDPI, vol. 8(1), pages 1-12, January.
    2. 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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