Rupture degree of graphs

Li, Yinkui; Zhang, Shenggui; Li, Xueliang

doi:10.1080/00207160412331336062

Cited by 59 publications

(36 citation statements)

References 4 publications

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“…Example 1 It can be easily seen that the vertex neighbour connectivity of a path P 9 and a comet C 6,6 are equal: VNC(P 9 ) = VNC(C 6,6 ) = 1.…”

Section: S⊆v (G)mentioning

confidence: 99%

“…Example 2 It can be easily seen that the vertex neighbour integrity of a cycle C 8 and a comet C 6,6 are equal: VNI(C 8 ) = VNI(C 6,6 ) = 3. On the other hand, the neighbour isolated scattering numbers of a cycle C 8 , a comet C 6,6 , and a path P 9 are different: NIS(P 9 ) = 1, NIS(C 8 ) = 0, and NIS(C 6,6 ) = 5.…”

Section: S⊆v (G)mentioning

confidence: 99%

“…On the other hand, the neighbour isolated scattering numbers of a cycle C 8 , a comet C 6,6 , and a path P 9 are different: NIS(P 9 ) = 1, NIS(C 8 ) = 0, and NIS(C 6,6 ) = 5.…”

Section: S⊆v (G)mentioning

confidence: 99%

“…In a network, the vulnerability parameters measure the resistance of the network to disruption of operation after the failure of certain stations or links. Parameters used to measure the vulnerability include connectivity, integrity 1 , scattering number 2 , isolated scattering number 3 , toughness 4 , tenacity 5 , and rupture degree 6 . However, most of these parameters do not consider the neighbourhoods of the effected vertices.…”

Section: Introductionmentioning

confidence: 99%

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Neighbour isolated scattering number of graphs

Aslan¹

2015

ScienceAsia

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ABSTRACT:The scattering number is a measure of the vulnerability of a graph. In this paper we investigate a refinement that involves the neighbour isolated version of the parameter. The neighbour isolated scattering number of a noncomplete graph G is defined to be NIS(G) = max{i(G/X )−|X | : i(G/X ) 1} where the maximum is taken over all X , the cut strategy of G, and i(G/X ) is the number of components which are isolated vertices of G/X . Like the scattering number itself, this is a measure of the vulnerability of a graph, but it is more sensitive. The relations between neighbour isolated scattering number and other parameters are determined and the neighbour isolated scattering number of trees and other families are obtained. We also give some results for the neighbour isolated scattering number of the graphs obtained by some graph operations.

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“…Example 1 It can be easily seen that the vertex neighbour connectivity of a path P 9 and a comet C 6,6 are equal: VNC(P 9 ) = VNC(C 6,6 ) = 1.…”

Section: S⊆v (G)mentioning

confidence: 99%

Section: S⊆v (G)mentioning

confidence: 99%

“…On the other hand, the neighbour isolated scattering numbers of a cycle C 8 , a comet C 6,6 , and a path P 9 are different: NIS(P 9 ) = 1, NIS(C 8 ) = 0, and NIS(C 6,6 ) = 5.…”

Section: S⊆v (G)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Neighbour isolated scattering number of graphs

Aslan¹

2015

ScienceAsia

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“…Based on these quantities, many graph parameters, such as connectivity, toughness [5], scattering number [14], integrity [1], tenacity [6], rupture degree [15] and edge-analogues of some of them, have been proposed for measuring the vulnerability of networks.…”

Section: Introductionmentioning

confidence: 99%

Extreme Tenacity of Graphs with Given Order and Size

Cheng

et al. 2014

J. Oper. Res. Soc. China

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Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured by various graph parameters, such as connectivity, toughness, scattering number, integrity, tenacity, rupture degree and edge-analogues of some of them. Among these parameters, the tenacity and rupture degree are two better ones to measure the stability of a network. In this paper, we consider two extremal problems on the tenacity of graphs: determine the minimum and maximum tenacity of graphs with given order and size. We give a complete solution to the first problem, while for the second one, it turns out that the problem is much more complicated than that of the minimum case. We determine the maximum tenacity of trees with given order and show the corresponding extremal graphs. The paper concludes with a discussion of a related problem on the edge vulnerability parameters of graphs.

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