Yazar "Turaci, Tufan" seçeneğine göre listele

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    THE AVERAGE LOWER REINFORCEMENT NUMBER OF A GRAPH
    (Edp Sciences S A, 2016) Turaci, Tufan; Aslan, Ersin
    Let G = (V (G), E(G)) be a simple undirected graph. The reinforcement number of a graph is a vulnerability parameter of a graph. We have investigated a refinement that involves the average lower reinforcement number of this parameter. The lower reinforcement number, denoted by r(e*) (G), is the minimum cardinality of reinforcement set in G that contains the edge e* of the complement graph G. The average lower reinforcement number of G is defined by r(av)(G) = 1/ |E(G)| Sigma(e*)is an element of E((G) over bar) r(e*) (G). In this paper, we define the average lower reinforcement number of a graph and we present the exact values for some well-known graph families.
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    Closeness centrality in some splitting networks
    (Inst Mathematics & Computer Science Acad, 2018) Aytac, Vecdi; Turaci, Tufan
    A central issue in the analysis of complex networks is the assessment of their robustness and vulnerability. A variety of measures have been proposed in the literature to quantify the robustness of networks, and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. Centrality parameters play an important role in the field of network analysis. Numerous studies have proposed and analyzed several centrality measures. We consider closeness centrality which is defined as the total graph-theoretic distance to all other vertices in the graph. In this paper, closeness centrality of some splitting graphs is calculated, and exact values are obtained.
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    Combining the Concepts of Residual and Domination in Graphs
    (Ios Press, 2019) Turaci, Tufan; Aytac, Aysun
    Let G = (V (G), E(G)) be a simple undirected graph. The domination and average lower domination numbers are vulnerability parameters of a graph. We have investigated a refinement that involves the residual domination and average lower residual domination numbers of these parameters. The lower residual domination number, denoted by gamma(R)(uk)(G), is the minimum cardinality of dominating set in G that received from the graph G where the vertex v(k) and all links of the vertex v(k) are deleted. The residual domination number of graphs G is defined as gamma(R)(G) = minv(k)is an element of V(G){gamma(R)(vk)(G)} . The average lower residual domination number of G is de- fined by gamma(R)(av)(G) = 1/vertical bar V(G)vertical bar Sigma(vk is an element of V(G)) gamma(R)(vk)(G). In this paper, we define the residual domination and the average lower residual domination numbers of a graph and we present the exact values, upper and lower bounds for some graph families.
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    Global distribution center number of some graphs and an algorithm
    (Edp Sciences S A, 2019) Durgut, Rafet; Kutucu, Hakan; Turaci, Tufan
    The global center is a newly proposed graph concept. For a graph G = (V(G), E(G)), a set S subset of V(G) is a global distribution center if every vertex v is an element of V(G)\S is adjacent to a vertex u is an element of S with |N[u] boolean AND S| >= |N[v] boolean AND (V(G)\S)|, where N(v) = {u is an element of V(G)|uv is an element of E(G)} and N[v] = N(v) ? {v}. The global distribution center number of a graph G is the minimum cardinality of a global distribution center of G. In this paper, we investigate the global distribution center number for special families of graphs. Furthermore, we develop a polynomial time heuristic algorithm to find the set of the global distribution center for general graphs.
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    A heuristic algorithm to find rupture degree in graphs
    (Tubitak Scientific & Technological Research Council Turkey, 2019) Durgut, Rafet; Turaci, Tufan; Kutucu, Hakan
    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 r(G) = max{omega(G - S) - vertical bar S vertical bar - m(G - S) : omega(G - S) >= 2, S subset of V}, where omega(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 NP- 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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    On Combining the Methods of Link Residual and Domination in Networks
    (Ios Press, 2020) Turaci, Tufan
    The concept of vulnerability is very important in network analysis. Several existing parameters have been proposed in the literature to measure network vulnerability, such as domination number, average lower domination number, residual domination number, average lower residual domination number, residual closeness and link residual closeness. In this paper, incorporating the concept of the domination number and link residual closeness number, as well as the idea of the average lower domination number, we introduce new graph vulnerability parameters called the link residual domination number, denoted by gamma(LR)(G), and the average lower link residual domination number, denoted by gamma(LR)(av) (G), for any given graph G. Furthermore, the exact values and the upper and lower bounds for any graph G are given, and the exact results of well-known graph families are computed.
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    ON THE AVERAGE LOWER BONDAGE NUMBER OF A GRAPH
    (Edp Sciences S A, 2016) Turaci, Tufan
    The domination number is an important subject that it has become one of the most widely studied topics in graph theory, and also is the most often studied property of vulnerability of communication networks. The vulnerability value of a communication network shows the resistance of the network after the disruption of some centers or connection lines until a communication breakdown. Let G = (V(G), E(G)) be a simple graph. The bondage number b(G) of a nonempty graph G is the smallest number of edges whose removal from G result in a graph with domination number greater than that of G. If we think a graph as a modeling of network, the average lower bondage number of a graph is a new measure of the graph vulnerability and it is defined by b(av)(G) = 1/vertical bar E(G)vertical bar Sigma(E is an element of(G)) b(e)(G), where the lower bondage number, denoted by b(e)(G), of the graph G relative to e is the minimum cardinality of bondage set in G that contains the edge e. In this paper, the above mentioned new parameter has been defined and examined. Then upper bounds, lower bounds and exact formulas have been obtained for any graph G. Finally, the exact values have been determined for some well-known graph families.
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    On the average lower bondage number of graphs under join and corona operations
    (Wiley, 2022) Turaci, Tufan; Kocay, Gamze
    Networks describe a wide range of systems in nature and society including examples the Internet, metabolic networks, electric power grids, supply chains, and the world trade Web among many others. The stability and reliability of a network are of prime importance to network designers. The domination number and its various, for example, bondage number, reinforcement number, etc. have been used network vulnerability parameters. Very recently, the average lower bondage number has been defined by Turaci in Reference [27]. In this paper, the average lower bondage number of the corona graphs and join graphs of given any two graphs G(1) and G(2) have been investigated, also exact formulas have been obtained.
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    ON THE DOMINATION, STRONG AND WEAK DOMINATION IN TRANSFORMATION GRAPH Gxy-
    (Util Math Publ Inc, 2019) Aytac, Aysun; Turaci, Tufan
    Let G = (V(G), E(G)) be a simple undirected graph of order vs and size m, and x, y, z be three variables taking value + or -. The transformation graph of G, G(xyz) is a simple graph having V(G) boolean OR E(G) as the vertex set. If an expression has n variables, and each variable can have the value + or -, the number of different combinations of values of the variables is 2(n). Thus, we obtain eight kinds of transformation graphs. A set S subset of V(G) is a dominating set if every vertex in V(G) - S is adjacent to at least one vertex in S. The minimum cardinality taken over all dominating sets of G is called the domination number of G and is denoted by gamma(G). There are several types of domination parameters depending upon the nature of dominating sets. In this paper, we investigate the domination number, the strong domination number and the weak domination number of the transformation graph G(xy)(-).
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    On topological properties of some molecular cactus chain networks and their subdivisions by using line operator
    (Taylor & Francis Ltd, 2022) Turaci, Tufan; Durgut, Rafet
    The mathematical chemistry is the part of theoretical chemistry which is concerned with applications of mathematical applications and methods to chemical problems. Graph theory is the most important part of mathematical chemistry. It studies of descriptors in quantitative structure property relationship (QSPR) and quantitative structure activity relationship (QSAR) studies in the chemistry science. Let G = (V(G), E(G)) be a chemical graph without directed and multiple edges and without loops. There are a lot of topological indices in QSPR/QSAR studies. In this paper, some degree-based topological indices namely first general Zagreb index, general Randic connectivity index, general sum-connectivity index, atom-bond connectivity index, geometric-arithmetic index, ABC (4)(G) index and GA (5)(G) index are computed for the line graphs and para-chain graphs of meta-chain M-n , para-chain L-n and ortho-chain O-n .
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    RELATIONSHIPS BETWEEN VERTEX ATTACK TOLERANCE AND OTHER VULNERABILITY PARAMETERS
    (Edp Sciences S A, 2017) Aytac, Vecdi; Turaci, Tufan
    Let G(V,E) be a simple undirected graph. Recently, the vertex attack tolerance (VAT) of G has been defined as ?(G) = min {|S| / |V-S-Cmax (G-S)|+1 : S ? V} , where Cmax(G - S) is the order of a largest connected component in G - S. This parameter has been used to measure the vulnerability of networks. The vertex attack tolerance is the only measure that fully captures both the major bottlenecks of a network and the resulting component size distribution upon targeted node attacks. In this article, the relationships between the vertex attack tolerance and some other vulnerability parameters, namely connectivity, toughness, integrity, scattering number, tenacity, binding number and rupture degree have been determined.
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    RESIDUAL CLOSENESS OF SPLITTING NETWORKS
    (Charles Babbage Res Ctr, 2017) Turaci, Tufan; Aytac, Vecdi
    Networks are important structures and appear in many different applications and settings. The vulnerability value of a communication network shows the resistance of the network after the disruption of some centers or connection lines until a communication breakdown. Centrality parameters play an important role in the field of network analysis. Numerous studies have proposed and analyzed several centrality measures. These concept measures 'the importance of a node's position in a network. In this paper, vertex residual closeness( VRC) and normalized vertex residual closeness(NVRC) of some Splitting networks modeling by splitting graph are obtained.
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    VULNERABIILITY OF MYCIELSKI GRAPHS VIA RESIDUAL CLOSENESS
    (Charles Babbage Res Ctr, 2015) Turaci, Tufan; Okten, Mukaddes
    The vulnerability value of a communication network is the resistance of this communication network until some certain stations or communication links between these stations are disrupted and, thus communication interrupts. A communication network is modeled by a graph to measure the vulnerability as stations corresponding to the vertices and communication links corresponding to the edges. There are several types of vulnerability parameters depending upon the distance for each pair of two vertices. In this paper, closeness, vertex residual closeness (VRC) and normalized vertex residual closeness (NV RC) of some Mycielski graphs are calculated, furthermore upper and lower bounds are obtained.
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    Vulnerability Measures of Transformation Graph Gxy+
    (World Scientific Publ Co Pte Ltd, 2015) Aytac, Aysun; Turaci, Tufan
    Several factors have to be taken into account in the design of large interconnection networks. Optimal design is important both to achieve good performance and to reduce the cost of construction and maintenance. Practical communication networks are exposed to failures of network components. Failures between nodes and connections happen and it is desirable that a network is robust in the sense that a limited number of failures does not break down the whole system. Robustness of the network topology is a key aspect in the design of computer networks. A variety of measures have been proposed in the literature to quantify the robustness of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. In this paper, we study the vulnerability of interconnection networks to the failure of individual nodes, using a graph-theoretic concept of domination and strong-weak domination numbers of the transformation graph G(xy)+ as a measure of network robustness.
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    The Vulnerability of Some Networks including Cycles via Domination Parameters
    (Hindawi Ltd, 2016) Turaci, Tufan; Aksan, Huseyin
    Let G = (V(G), E(G)) be an undirected simple connected graph. A network is usually represented by an undirected simple graph where vertices represent processors and edges represent links between processors. Finding the vulnerability values of communication networks modeled by graphs is important for network designers. The vulnerability value of a communication network shows the resistance of the network after the disruption of some centers or connection lines until a communication breakdown. The domination number and its variations are the most important vulnerability parameters for network vulnerability. Some variations of domination numbers are the 2-domination number, the bondage number, the reinforcement number, the average lower domination number, the average lower 2-domination number, and so forth. In this paper, we study the vulnerability of cycles and related graphs, namely, fans, k-pyramids, and n-gon books, via domination parameters. Then, exact solutions of the domination parameters are obtained for the above-mentioned graphs.
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    ZAGREB ECCENTRICITY INDICES OF CYCLES RELATED GRAPHS
    (Charles Babbage Res Ctr, 2016) Turaci, Tufan
    Graph theory, with its diverse applications in theoretical computer science and in natural (Chemistry, Biology) in particular is becoming an important component of the mathematics. Recently, the concepts of new zagreb eccentricity indices were introduced. These indices were defined for any graph G, as follows: M-1*(G) = Sigma(euv is an element of E(G))[epsilon(G)(u) + epsilon(G)(v)] (G) = M-1**(G) = Sigma(v is an element of V)[epsilon(G)(v)](2) and M-2*(G) = Sigma(euv is an element of E(G))[epsilon(G)(u) epsilon(G)(v)], where epsilon(G)(u) is eccentricity value of vertex u in the graph G. In this paper, new zagreb eccentricity indices M-1*(G), M-1**(G) and M-2*(G) of cycles related graphs namely gear, friendship and corona graphs are determined. Then, a programming code finding values of new zagreb indices of any graph is offered.