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Isolation Number of Transition Graphs

Author

Listed:
  • Junhao Qu

    (School of Mathematics and Statistics, Qinghai Normal University, Xining 810001, China
    These authors contributed equally to this work.)

  • Shumin Zhang

    (School of Mathematics and Statistics, Qinghai Normal University, Xining 810001, China
    Academy of Plateau Science and Sustainability, People’s Government of Qinghai Province and Beijing Normal University, Qinghai Normal University, Xining 810008, China
    These authors contributed equally to this work.)

Abstract

Let G = ( V , E ) be a graph and F be a family of graphs; a subset ( S ⊆ V ( G ) ) is said to be an F -isolating set if G [ V ( G ) ∖ N G [ S ] ] does not contain F as a subgraph for all F ∈ F . The F -isolation number of G is the minimum cardinality of an F -isolating set ( S ) of G , denoted by ι ( G , F ) . When F = { K 1 , k + 1 } , we use ι k ( G ) to define the F -isolation number ( ι ( G , F ) ). In particular, when k = 0 , we use the short form of ι ( G ) instead of ι 0 ( G ) . A subset ( S ⊆ V ( G ) ) is called an isolating set if V ( G ) ∖ N G [ S ] is an independent set of G . The isolation number of G is the minimum cardinality of an isolating set, denoted by ι ( G ) . In this paper, we mainly focus on research on the isolation number and F -isolation number of a B ( G ) graph, total graph and central graph of graph G .

Suggested Citation

  • Junhao Qu & Shumin Zhang, 2024. "Isolation Number of Transition Graphs," Mathematics, MDPI, vol. 13(1), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:116-:d:1557206
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    References listed on IDEAS

    as
    1. Xu Zhu & Jieun Yu & Wonjun Lee & Donghyun Kim & Shan Shan & Ding-Zhu Du, 2010. "New dominating sets in social networks," Journal of Global Optimization, Springer, vol. 48(4), pages 633-642, December.
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