On the Rupture Degree of a Graph

Kirlangic, Alpay; Bacak-Turan, Gökşen

doi:10.14311/nnw.2012.22.003

Cited by 4 publications

(2 citation statements)

References 9 publications

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“…However, it is possible to determine the rupture degree of large classes of graphs. For more results on rupture degree, we refer the readers to see [16][17][18][19][20][21]. Furthermore, Li gave an algorithm whose complexity is O(n 2 ) for isolating rupture degree in Trees of order n [22].…”

Section: Introductionmentioning

confidence: 99%

A heuristic algorithm to find rupture degree in graphs

Durgut¹,

Turaci²,

Kutucu³

2019

Turk J Elec Eng & Comp Sci

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Since the problem of Konigsberg bridge was released in 1735, there have been many applications of graph theory in mathematics, physics, biology, computer science, and several fields of engineering. In particular, all communication networks can be modeled by graphs. The vulnerability is a concept that represents the reluctance of a network to disruptions in communication after a deterioration of some processors or communication links. Furthermore, the vulnerability values can be computed with many graph theoretical parameters. The rupture degree r(G) of a graph G = (V, E) is an important graph vulnerability parameter and defined as rwhere ω(G − S) and m(G − S) denote the number of connected components and the size of the largest connected component in the graph G − S , respectively. Recently, it has been proved that finding the rupture degree problem is N P -complete. In this paper, a heuristic algorithm to determine the rupture degree of a graph has been developed. Extensive computational experience on 88 randomly generated graphs ranging from 20% to 90% densities and from 100 to 200 vertices shows that the proposed algorithm is very effective.

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Section: Introductionmentioning

confidence: 99%

A heuristic algorithm to find rupture degree in graphs

Durgut¹,

Turaci²,

Kutucu³

2019

Turk J Elec Eng & Comp Sci

View full text Add to dashboard Cite

show abstract

“…The communication network can be represented as an undirected and unweighted graph, where a processor (station) is represented as a vertex and a communication link between processors (stations) as an edge between corresponding vertices. If we use a graph to model a network, based on the above three quantities, a number of graph parameters, such as connectivity [2], toughness [5], scattering number [7,17], integrity [1], tenacity [6], rupture degree [8,10,11,12,14] and their edge-analogues, have been proposed for measuring the vulnerability of networks.…”

Section: Introductionmentioning

confidence: 99%

Isolated Rupture Degree of Trees and Gear Graphs

Li¹

2015

NNW

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The isolated rupture degree for a connected graph G is defined as ir(G) = max{i(G−S)−|S|−m(G−S) : S ∈ C(G)}, where i(G−S) and m(G−S), respectively, denote the number of components which are isolated vertices and the order of a largest component in G − S. C(G) denotes the set of all cut-sets of G. The isolated rupture degree is a new graph parameter which can be used to measure the vulnerability of networks. In this paper, we firstly give a recursive algorithm for computing the isolated rupture degree of trees, and determine the maximum and minimum isolated rupture degree of trees with given order and maximum degree. Then, the exact value of isolated rupture degree of gear graphs are given. In the final, we determine the rupture degree of the Cartesian product of two special graphs and a special permutation graph.

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Weak-Rupture Degree of Graphs

Aslan

2016

Int. J. Found. Comput. Sci.

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The rupture degree of a graph is a measure of the vulnerability of a graph. In this paper we investigate a refinement that involves the weak version of the parameter. The weak-rupture degree of a connected graph G is defined to be [Formula: see text] where [Formula: see text] is the number of the components of [Formula: see text] and [Formula: see text] is the number of edges of the largest component of [Formula: see text]. Like the rupture degree itself, this is a measure of the vulnerability of a graph, but it is more sensitive. This paper, the weak-rupture degree of some special graphs are obtained and some bounds of the weak-rupture degree are given. Moreover some results about the weak-rupture degree of graphs obtained by graph operations are given.

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On the Rupture Degree of a Graph

Cited by 4 publications

References 9 publications

A heuristic algorithm to find rupture degree in graphs

A heuristic algorithm to find rupture degree in graphs

Isolated Rupture Degree of Trees and Gear Graphs

Weak-Rupture Degree of Graphs

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