Geodesic
Relationships between vertex attack tolerance and other vulnerability parameters
Aytaç, Vecdi1 ; Turaci, Tufan2
1 Computer Engineering Department Faculty of Engineering, Ege University, 35100, Bornova-IZMIR, Turkey
2 Department of Mathematics, Faculty of Science, Karabük University, 78050, Karabük, Turkey
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 51 (2017) no. 1, pp. 17-27

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Let G(V,E) be a simple undirected graph. Recently, the vertex attack tolerance (VAT) of G has been defined as τ(G) = min {|S| / |V-S-Cmax (G-S)|+1 : S ⊂ V} , where C max (G-S) is the order of a largest connected component in G-S. This parameter has been used to measure the vulnerability of networks. The vertex attack tolerance is the only measure that fully captures both the major bottlenecks of a network and the resulting component size distribution upon targeted node attacks. In this article, the relationships between the vertex attack tolerance and some other vulnerability parameters, namely connectivity, toughness, integrity, scattering number, tenacity, binding number and rupture degree have been determined.

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DOI : 10.1051/ita/2017005
Classification : 05C40, 68M10, 68R10
Keywords: Graph vulnerability, vertex attack tolerance, connectivity, network design and communication, toughness, integrity, scattering number, tenacity, binding number, rupture degree

Aytaç, Vecdi 1 ; Turaci, Tufan 2

1 Computer Engineering Department Faculty of Engineering, Ege University, 35100, Bornova-IZMIR, Turkey
2 Department of Mathematics, Faculty of Science, Karabük University, 78050, Karabük, Turkey 
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Aytaç, Vecdi; Turaci, Tufan. Relationships between vertex attack tolerance and other vulnerability parameters. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 51 (2017) no. 1, pp. 17-27. doi: 10.1051/ita/2017005

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