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Bounds for scattering number and rupture degree of graphs with genus

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  • Li, Yinkui
  • Gu, Ruijuan

Abstract

For a given graph G=(V,E), denote by m(G) and ω(G) the order of the largest component and the number of components of G, respectively. The scattering number of G is defined as s(G)=max{ω(G−X)−|X|:X⊆V,ω(G−X)>1}, and the rupture degree r(G)=max{ω(G−X)−|X|−m(G−X):X⊆V(G),ω(G−X)>1}. These two parameters are related to reliability and vulnerability of networks. In this paper, we present some new bounds on the scattering number and rupture degree of a graph G in terms of its connectivity κ(G) and genus γ(G). Furthermore, we give graphs to show these bounds are best possible.

Suggested Citation

  • Li, Yinkui & Gu, Ruijuan, 2018. "Bounds for scattering number and rupture degree of graphs with genus," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 329-334.
    • Handle: RePEc:eee:apmaco:v:337:y:2018:i:c:p:329-334
    DOI: 10.1016/j.amc.2018.05.023
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    References listed on IDEAS

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    1. Lan, Yongxin & Li, Tao & Ma, Yuede & Shi, Yongtang & Wang, Hua, 2018. "Vertex-based and edge-based centroids of graphs," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 445-456.
    2. Lei, Hui & Li, Tao & Ma, Yuede & Wang, Hua, 2018. "Analyzing lattice networks through substructures," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 297-314.
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    Cited by:

    1. Abolfazl Javan & Ali Moeini & Mohammad Shekaramiz, 2024. "Tightness of Harary Graphs," Mathematics, MDPI, vol. 12(18), pages 1-12, September.

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