Browsing by Author "Aytac, Aysun"

Now showing 1 - 5 of 5

Citation - WoS: 8
Citation - Scopus: 12
The Bondage Number of Some Graphs
(Publ House Bulgarian Acad Sci, 2011) Aytac, Aysun; Odabas, Zeynep Nihan; Turaci, Tufan
The stability of a communication network, composed of processing nodes and communication links, is of prime importance to network designers. On description of the network resistance, finding critical vertices or links, are written many papers. In 1970s different measures of the graph vulnerability are introduced to study different aspects of the graph behaviour after removal of vertices or links. The domination number is one of these measures. Different types of domination parameters are defined such as bondage, reinforcement, strong-weak domination, strong-weak bondage numbers. In this paper, firstly we investigate strong-weak domination number of corona and gear graphs. Then several results for the bondage, strong-weak bondage of corona and gear graphs are obtained.
Citation - WoS: 7
Citation - Scopus: 6
Computing the Rupture Degree in Composite Graphs
(World Scientific Publ Co Pte Ltd, 2010) Aytac, Aysun; Odabas, Zeynep Nihan
The rupture degree of an incomplete connected graph G is defined by r (G) = max {w (G - S) - vertical bar S vertical bar - m (G - S) : S subset of V (G), w (G - S) > 1} where w (G - S) is the number of components of G - S and m (G - S) is the order of a largest component of G - S. For the complete graph K(n); rupture degree is defined as 1 - n. This parameter can be used to measure the vulnerability of a graph. Rupture degree can reflect the vulnerability of graphs better than or independent of the other parameters. To some extent, it represents a trade-off between the amount of work done to damage the network and how badly the network is damaged. Computing the rupture degree of a graph is NP-complete. In this paper, we give formulas for the rupture degree of composition of some special graphs and we consider the relationships between the rupture degree and other vulnerability parameters.
Citation - WoS: 36
Citation - Scopus: 32
Residual Closeness in Cycles and Related Networks
(Ios Press, 2013) Berberler, Zeynep Nihan; Aytac, Aysun
Networks are known to be prone to node or link failures. A central issue in the analysis of networks is the assessment of their stability and reliability. The main aim is to understand, predict, and possibly even control the behavior of a networked system under attacks or disfunctions of any type. A central concept that is used to assess stability and robustness of the performance of a network under failures is that of vulnerability. A network is usually represented by an undirected simple graph where vertices represent processors and edges represent links between processors. Different approaches to properly define a measure for graph vulnerability has been proposed so far. In this paper, we study the vulnerability of cycles and related graphs to the failure of individual vertices, using a measure called residual closeness which provides a more sensitive characterization of the graph than some other well-known vulnerability measures.
Citation - WoS: 36
Citation - Scopus: 36
Residual Closeness of Wheels and Related Networks
(World Scientific Publ Co Pte Ltd, 2011) Aytac, Aysun; Odabas, Zeynep Nihan
The vulnerability of a network measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. If we think of a graph as modeling a network, several vulnerability measures have been used to describe the stability of networks, including connectivity, toughness, scattering number, binding number and integrity. We consider a new characteristic, residual closeness which is more sensitive than the well-known vulnerability measures. Residual closeness measures the network resistance evaluating closeness after removal of vertices or links. In this paper, closeness, vertex residual closeness (VRC) and normalized vertex residual closeness (NVRC) of wheels and some related networks namely gear and friendship graph are calculated, and exact values are obtained.
Citation - WoS: 4
Citation - Scopus: 4
Rupture Degree and Middle Graphs
(Publ House Bulgarian Acad Sci, 2012) Odabas, Zeynep Nihan; Aytac, Aysun
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 parameters like connectivity, toughness, integrity, tenacity and scattering number. The rupture degree of a graph is a new parameter to measure the vulnerability of networks. For the complete graph K, rupture degree is defined as 1-n and for an incomplete connected graph G, rupture degree is defined by r(G) = max{w(G-S)-vertical bar S vertical bar-m(G-S) : S subset of V(G), w(G-S) > 1}, where w(G - S) is the number of components of G S and in m(G - S) is the order of a largest component of G - S. Rupture degree is independent from the other vulnerability parameters. In this paper, rupture degree of middle graphs is considered.