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Extra Edge Connectivity and Extremal Problems in Education Networks

Author

Listed:
  • Hongfang Liu

    (School of Education, Shaanxi Normal University, Xi’an 710062, China
    School of Education, Qinghai Normal University, Xining 810008, China)

  • Jinxia Liang

    (School of Mathematics and Statistics, Qinghai Normal University, Xining 810008, China)

  • Kinkar Chandra Das

    (Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea)

Abstract

Extra edge connectivity and diagnosability have been employed to investigate the fault tolerance properties of network structures. The p -extra edge connectivity λ p ( Γ ) of a graph Γ was introduced by Fàbrega and Fiol in 1996. In this paper, we find the exact values of p -extra edge connectivity of some special graphs. Moreover, we give some upper and lower bounds for λ p ( Γ ) , and graphs with λ p ( Γ ) = 1 , 2 , n 2 n 2 − 1 , n 2 n 2 are characterized. Finally, we obtain the three extremal results for the p -extra edge connectivity.

Suggested Citation

  • Hongfang Liu & Jinxia Liang & Kinkar Chandra Das, 2022. "Extra Edge Connectivity and Extremal Problems in Education Networks," Mathematics, MDPI, vol. 10(19), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3475-:d:923326
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    Cited by:

    1. Hongfang Liu & Zhizhang Shen & Chenxu Yang & Kinkar Chandra Das, 2022. "On a Combinatorial Approach to Studying the Steiner Diameter of a Graph and Its Line Graph," Mathematics, MDPI, vol. 10(20), pages 1-18, October.

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