Browsing by Publisher "EDP SCIENCES S A"

Now showing 1 - 6 of 6
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    NEIGHBOR ISOLATED TENACITY OF GRAPHS
    (EDP SCIENCES S A) 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 NIT (G) = min{vertical bar X vertical bar+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.
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    THE AVERAGE LOWER REINFORCEMENT NUMBER OF A GRAPH
    (EDP SCIENCES S A) Turaci, T; Aslan, E
    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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    Weak and strong domination on some graphs
    (EDP SCIENCES S A) Durgun, DD; Kurt, BL
    Let G = (V(G), E(G)) be a graph and uv epsilon E. A subset D subset of V of vertices is a dominating set if every vertex in V - D is adjacent to at least one vertex of D. The domination number is the minimum cardinality of a dominating set. Let u and v be elements of V. Then, u strongly dominates u and v weakly dominates u if (i)uv epsilon E and (ii)deg(u) >= deg(v). A set D subset of V is a strong (weak) dominating set (sd-set)(wd-set) of G if every vertex in V - D is strongly dominated by at least one vertex in D. The strong (weak) domination number gamma(s)(gamma(w)) of G is the minimum cardinality of a sd-set (wd-set). In this paper, the strong and weak domination numbers of comet, double comet, double star and theta graphs are given. The theta graphs are important geometric graphs that have many applications, including wireless networking, motion planning, MST construction and real-time animation.
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    An investigation of cutting parameters effect on sound level, surface roughness, and power consumption during machining of hardened AISI 4140
    (EDP SCIENCES S A) Sahinoglu, A; Ulas, E
    In recent years, the necessity for energy in the manufacturing industry has become an important problem because fossil fuel reserves are decreasing in order to produce energy. Therefore, the efficient use of energy has become an important research topic. In this study, energy efficiency is investigated in detail for sustainable life and manufacturing. AISI 4140 material with high hardness of 50 HRC hardness has been applied cryogenic process to improve mechanical and machinability properties. In this experiment study, the effects of feed rate (0.04, 0.08, 0.12 mm/rev), cutting speed (140, 160, 180 m/min), depth of cut (0.05, 0.10, 0.15 mm) and tool radius (0.4, 0.8) on energy consumption, surface roughness and sound intensity were investigated. Then, a new mathematical model with high accuracy was developed. Total power consumption was calculated by considering the instantaneous current value and machining time. As a result, it is found that good surface quality obtained when the feed rate is low, and the tool radius is high and the machining time is shortened, the energy consumption is reduced due to the increase in cutting speed, depth of cut and feed rate. Also, it is found that the tool radius has a limited effect on energy consumption, but low feed value increases energy consumption.
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    AVERAGE COVERING NUMBER FOR SOME GRAPHS
    (EDP SCIENCES S A) Durgun, DD; Bagatarhan, A
    The interconnection networks are modeled by means of graphs to determine the reliability and vulnerability. There are lots of parameters that are used to determine vulnerability. The average covering number is one of them which is denoted by (beta) over bar (G) , where G is simple, connected and undirected graph of order n >= 2. In a graph G = (V (G), E(G)) a subset S-v subset of V (G) of vertices is called a cover set of G with respect to v or a local covering set of vertex v, if each edge of the graph is incident to at least one vertex of S-v. The local covering number with respect to v is the minimum cardinality of among the S-v sets and denoted by beta(v) The average covering number of a graph G is defined as (beta) over bar (G) = 1/vertical bar V(G)vertical bar Sigma(v is an element of V(G)) beta(v). In this paper, the average covering numbers of kth power of a cycle C-n(k) and P-n square p(m), P-n, square C-m, cartesian product of P-n, and P-m cartesian product of P-n, and C-m are given, respectively.
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    THE AVERAGE SCATTERING NUMBER OF GRAPHS
    (EDP SCIENCES S A) Aslan, E; Kilinç, D; Yücalar, F; Borandag, 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 sc(v)(G) = max{omega(G - S-v) - vertical bar S-v vertical bar},where the maximum is taken over all disconnecting sets S-v of G that contain v. The average scattering number of G denoted by sc(av)(G), is defined as sc(av)(G) = Sigma v is an element of V(G)sc(v)(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.