Bounds for scattering number and rupture degree of graphs with genus

Yinkui Li and Ruijuan Gu

Applied Mathematics and Computation, 2018, vol. 337, issue C, 329-334

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.

Keywords: Scattering number; Rupture degree; Connectivity; Genus (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:337:y:2018:i:c:p:329-334

DOI: 10.1016/j.amc.2018.05.023

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