Browsing by Author "Bacak-Turan G."
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Item Graph operations and neighbor rupture degree(2013) Kandilci S.; Bacak-Turan G.; Polat R.In a communication network, the vulnerability parameters measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. A vertex subversion strategy of a graph G, say S, is a set of vertices in G whose closed neighborhood is removed from G. The survival subgraph is denoted by G/S. The neighbor rupture degree of G, Nr(G), is defined to be Nr (G) =max{w(G/S) -|S| - c(G/S): S ⊂ V(G), w(G/S) ≥1}, where S is any vertex subversion strategy of G, w(G/S) is the number of connected components in G/S and c(G/S) is the maximum order of the components of G/S (G. Bacak Turan, 2010). In this paper we give some results for the neighbor rupture degree of the graphs obtained by some graph operations. © 2013 Saadet Kandİlcİ et al.Item Neighbor integrity of transformation graphs(2013) Bacak-Turan G.; Kirlangic A.In a communication network, the vulnerability measures are essential to guide the designer in choosing an appropriate topology. They measure the stability of the network to disruption of operation after the failure of certain stations or communication links. If a station or operative is captured in a spy network, then the adjacent stations will be betrayed and are therefore useless in the whole network. In this sense, Margaret B. Cozzens and Shu-Shih Y. Wu modeled a spy network as a graph and then defined the neighbor integrity of a graph to obtain the vulnerability of a spy network [10]. The neighbor integrity of a graph G, is defined to be $NI(G)=\displaystyle{\min-{S\subseteq V(G)}\{|S|+c(G/S)\}}$, where S is any vertex subversion strategy of G and c(G/S) is the maximum order of the components of G/S. In this paper, we investigate the transformation graphs G-+-, G+-, G ++-, G- -, G+-+, G-++, G -+ and G+++ of a graph G, and determine their neighbor integrity. © 2013 World Scientific Publishing Company.Item Neighbor Rupture Degree of Harary Graphs(World Scientific Publishing Co. Pte Ltd, 2016) Altundag F.N.; Bacak-Turan G.The vulnerability shows the endurance of the network until the communication collapse after the breakdown of certain stations or communication links. If a spy or a station is invaded in a spy network, then the adjacent stations are treacherous. A vulnerability parameter the neighbor rupture degree can be used to obtain the vulnerability of a spy network. The neighbor rupture degree of a noncomplete connected graph G is defined to be Nr(G) = max{w(G/S) - |S| - c(G/S): S SV (G),w(G/S) ≥ 1} where S is any vertex subversion strategy of G, w(G/S) is the number of connected components in G/S, and c(G/S) is the maximum order of the components of G/S. In this paper, the neighbor rupture degree of Harary graphs are obtained. © 2016 World Scientific Publishing Company.Item 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.Item Neighbor Rupture Degree of Transformation Graphs Gxy-(World Scientific Publishing Co. Pte Ltd, 2017) Bacak-Turan G.; Oz E.A vulnerability parameter the neighbor rupture degree can be used to obtain the vulnerability of a spy network. The neighbor rupture degree of a noncomplete connected graph G is defined to be (Equation presented) where S is any vertex subversion strategy of G, w(G/S) is the number of connected components in G/S, and c(G/S) is the maximum order of the components of G/S. In this study, the neighbor rupture degree of transformation graphs G-, G+-, G-+- and G++- of path graphs, cycle graphs, wheel graphs, complete graphs and complete bipartite graphs are obtained. © 2017 World Scientific Publishing Company.Item Feasible Sanitary Sewer Network Generation Using Graph Theory(Hindawi Limited, 2019) Turan M.E.; Bacak-Turan G.; Cetin T.; Aslan E.A graph theory-based methodology is proposed for the sewer system optimization problem in this study. Sewer system optimization includes two subproblems: layout optimization and hydraulic design optimization, which can be solved independently or solved simultaneously. No matter which method is chosen for the solution of the optimization problem, a feasible layout that satisfies the restrictions of the sewer system must be obtained in any step of the solution. There are two different layout options encountered: the layouts containing all sewer links and the layouts not containing all sewer links. The method proposed in this study generates a feasible sewer layout that contains all sewer links and satisfies all restrictions of a sanitary sewer system by using graph theory without any additional strategies unlike other studies. The method is applied to two different case studies. The results of the case studies have shown that graph theory is well applicable to sewer system optimization and the methodology proposed based on it is capable of generating a feasible layout. This study is expected to stimulate the use of graph theory on similar studies. © 2019 Mustafa Erkan Turan et al.Item A study on vulnerability parameters of signed fuzzy graphs(Springer Verlag, 2020) Sundareswaran R.; Sujatha R.; Bacak-Turan G.Vulnerability is an important concept in network analysis. The concept of vulnerability parameters in signed fuzzy graphs is not addressed in the literature so far. In this paper, the vertex integrity of fuzzy signed graph is introduced and illustrated with an example. Also, some bounds of this parameter are discussed. © 2020, Springer Nature Switzerland AG.Item Domination integrity and efficient fuzzy graphs(Springer, 2020) Mariappan S.; Ramalingam S.; Raman S.; Bacak-Turan G.In this paper, domination integrity of fuzzy graph and efficient fuzzy graph concepts is introduced with examples. An algorithm is developed to find whether an arc is strong or not. If it is strong, another algorithm will classify it as α strong arc and β strong arc. The next algorithm is used to find whether the given fuzzy graph is a fuzzy tree or not. Domination and integrity are two different parameters used to define the stability of a graph in various situations. Using the strong arc concept a new parameter, domination integrity is defined and lower and upper bounds are found. This paper discusses the domination integrity for standard graphs such as path, cycle and complete graph. The domination integrity for Cartesian product of fuzzy graphs is also discussed. Finally, the new class of fuzzy graph, efficient fuzzy graph, is introduced. Efficient fuzzy graph is a special type of fuzzy graph that has the same dominating set, other than vertex set V, for both fuzzy graph and its underlying crisp graph. © 2019, Springer-Verlag London Ltd., part of Springer Nature.Item Vulnerability of sewer network – graph theoretic approach(Desalination Publications, 2020) Ganesan B.; Raman S.; Ramalingam S.; Turan M.E.; Bacak-Turan G.One of the most important structures in urban areas is an efficient sewer system to protect humans and the environment from the detrimental effects of wastewater. Such sewer systems often consist of pipes, manholes, pumping stations, and other complementary units. Strict monitoring of the sewer system is highly essential as any leakage can cause undesirable effects on health and safety. The layout is modeled as a graph which contains all sewer links and satisfies all the restrictions of a sanitary sewer system. In this work, we apply centrality measures on the sewer network system and water distribution system and also analyze the vulnerability of these systems. © 2020 Desalination Publications. All rights reserved.