Browsing by Subject "Rupture degree"

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    Mean rupture degree of graphs
    (Politechnica University of Bucharest, 2016) Aslan E.; Bacak-Turan G.
    The vulnerability shows the resistance of the network until communication breakdown after the disruption of certain stations or communication links. We introduce a new graph parameter, the mean rupture degree. Let G be a graph of order p and S be a subset of V(G). The graph G-S contains at least two components and if each one of the components of G-S have orders p1, p2,pk, then m(G-S)=Σtk=pi2/Σtk=pt Formally, the mean rupture degree of a graph G, denoted mr(G), is defined as mr(G)=max-ω(G-S)-|S|- (G-S): SV(G), ω(G-S)1} where ω(G-S) denote the number of components. In this paper, the mean rupture degree of some classes of graphs are obtained and the relations between mean rupture degree and other parameters are determined.
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    Neighbor isolated tenacity of graphs
    (EDP Sciences, 2016) Aslan E.
    The tenacity of a graph is a measure of the vulnerability of a graph. In this paper we investigate a refinement that involves the neighbor isolated version of this parameter. The neighbor isolated tenacity of a noncomplete connected graph G is defined to be {x+c(G/X)/i(G/X), i(G/X) ≥1} where the minimum is taken over all X, the cut strategy of G, i(G/X)is the number of components which are isolated vertices of G/X and c(G/X) is the maximum order of the components of G/X. Next, the relations between neighbor isolated tenacity and other parameters are determined and the neighbor isolated tenacity of some special graphs are obtained. Moreover, some results about the neighbor isolated tenacity of graphs obtained by graph operations are given. © EDP Sciences 2016.
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    The average scattering number of graphs
    (EDP Sciences, 2016) Aslan E.; Kilinç D.; Yücalar F.; Borandaǧ E.
    The scattering number of a graph is a measure of the vulnerability of a graph. In this paper we investigate a refinement that involves the average of a local version of the parameter. If v is a vertex in a connected graph G, then scv(G) = max {ω(G - Sv) - | Sv |}, where the maximum is taken over all disconnecting sets Sv of G that contain v. The average scattering number of G denoted by scav(G), is defined as scav(G) = Σv ϵ V(G) scv(G) / n, where n will denote the number of vertices in graph G. Like the scattering number itself, this is a measure of the vulnerability of a graph, but it is more sensitive. Next, the relations between average scattering number and other parameters are determined. The average scattering number of some graph classes are obtained. Moreover, some results about the average scattering number of graphs obtained by graph operations are given. © EDP Sciences 2016.