Browsing by Author "Aslan E."

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    Edge-neighbor-rupture degree of graphs
    (2013) Aslan E.
    The edge-neighbor-rupture degree of a connected graph G is defined to be ENRG=maxωG-S-S-mG-S:SEG,ωG-S≥1, where S is any edge-cut-strategy of G, ωG-S is the number of the components of G-S, and mG-S is the maximum order of the components of G-S. In this paper, the edge-neighbor-rupture degree of some graphs is obtained and the relations between edge-neighbor-rupture degree and other parameters are determined. © 2013 Ersin Aslan.
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    The average lower connectivity of graphs
    (2014) Aslan E.
    For a vertex v of a graph G, the lower connectivity, denoted by sv(G), is the smallest number of vertices that contains v and those vertices whose deletion from G produces a disconnected or a trivial graph. The average lower connectivity denoted by av(G) is the value (vVGsvG)/VG. It is shown that this parameter can be used to measure the vulnerability of networks. This paper contains results on bounds for the average lower connectivity and obtains the average lower connectivity of some graphs. © 2014 Ersin Aslan.
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    On the fourth atom-bond connectivity index of nanocones
    (National Institute of Optoelectronics, 2015) Aslan E.
    Atom bond connectivity index is a topological index was defined as ABC(G) = (Formula Present) where d(v) denotes the degree of vertex v of G. Recently, M. Ghorbani et al. introduced a new version of atom-bond connectivity (ABC4) index as ABC4(G) = (Formula Present) where Su=∑vεENG(u) dv and NG(u) = {v εV(G)luv ε(G)}. In this paper we compute the fourth atom-bond connectivity index for nanocones. © 2015, National Institute of Optoelectronics. All rights reserved.
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    Edge-rupture degree of a graph
    (Watam Press, 2015) Aslan E.
    The edge-rupture degree of a noncomplete connected graph G is defined to be r'(G) = max{ω(G - S) - |S| - m(G - S): S ⊆ E(G), ω(G - S) > 1} where ω(G - S) denote the number of components and m(G - S) denote the order of a largest component in G - S. In this paper, the relations between edge-rupture degree and other parameters are determined, and the edge-rupture degree of some graphs are obtained. Copyright © 2015 Watam Press.
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    The edge eccentric connectivity index of armchair polyhex nanotubes
    (American Scientific Publishers, 2015) Aslan E.
    Let f = uv be an edge in E(G). Then the degree of the edge f is defined to be deg(u)+deg(v)-2. For two edges f1 = u1v1, f2 = u2v2 in E(G), the distance between f1 and f2, denoted by ed (f1, f2), is defined to be ed (f1, f2) = min{d(u1, v1),d(u1, v2), d(u2, v1), d(u2, v2). The edge eccentricity of an edge f, denoted by ec (f), is defined as ec(f) = max{d(f, e) | e ϵ E(G)}. The edge eccentric connectivity index of G, denoted by ζc e(G) is defined as ζce(G) = Σ fϵE(G) deg(f)ec(f). In this paper exact formulas for the edge eccentric connectivity index of an armchair polyhex nanotube is given. © 2015 American Scientific Publishers.
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    Neighbour isolated scattering number of graphs
    (Science Society of Thailand under Royal Patronage, 2015) Aslan E.
    The scattering number is a measure of the vulnerability of a graph. In this paper we investigate a refinement that involves the neighbour isolated version of the parameter. The neighbour isolated scattering number of a noncomplete graph G is defined tobe NIS(G) = max{i(G/X)-|X|: i(G/X) ≥ 1} where the maximum is taken over all X, the cut strategy of G, and i(G/X) is the number of components which are isolated vertices of G/X. Like the scattering number itself, this is a measure of the vulnerability of a graph, but it is more sensitive. The relations between neighbour isolated scattering number and other parameters are determined and the neighbour isolated scattering number of trees and other families are obtained. We also give some results for the neighbour isolated scattering number of the graphs obtained by some graph operations.
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    The average lower reinforcement number of a graph
    (EDP Sciences, 2016) 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 re∗(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 rav (G)=1/E(G) ∑e∗∈E(G) re∗(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. © EDP Sciences 2016.
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    Neighbor isolated tenacity of graphs
    (EDP Sciences, 2016) 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 {x+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. © EDP Sciences 2016.
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    Weak-Rupture Degree of Graphs
    (World Scientific Publishing Co. Pte Ltd, 2016) Aslan E.
    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 R(G) = max{ (G-S)-| S |-me(G-S): S V (G),(G-S) > 1 } where(G-S) is the number of the components of (G-S) and me(G-S) is the number of edges of the largest component of G-S. 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. © 2016 World Scientific Publishing Company.
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    The average scattering number of graphs
    (EDP Sciences, 2016) Aslan E.; Kilinç D.; Yücalar F.; Borandaǧ 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 scv(G) = max {ω(G - Sv) - | Sv |}, where the maximum is taken over all disconnecting sets Sv of G that contain v. The average scattering number of G denoted by scav(G), is defined as scav(G) = Σv ϵ V(G) scv(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. © EDP Sciences 2016.
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    A numerical approach with error estimation to solve general integro-differential-difference equations using Dickson polynomials
    (Elsevier Inc., 2016) Kürkçü Ö.K.; Aslan E.; Sezer M.
    In this paper, a matrix method based on the Dickson polynomials and collocation points is introduced for the numerical solution of linear integro-differential-difference equations with variable coefficients under the mixed conditions. In addition, in order to improve the numerical solution, an error analysis technique relating to residual functions is performed. Some linear and nonlinear numerical examples are given to illustrate the accuracy and applicability of the method. Eventually, the obtained results are discussed according to the parameter-α of Dickson polynomials and the residual error estimation. © 2015 Elsevier Inc. All rights reserved.
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    Multi-level reranking approach for bug localization
    (Blackwell Publishing Ltd, 2016) Kılınç D.; Yücalar F.; Borandağ E.; Aslan E.
    Bug fixing has a key role in software quality evaluation. Bug fixing starts with the bug localization step, in which developers use textual bug information to find location of source codes which have the bug. Bug localization is a tedious and time consuming process. Information retrieval requires understanding the programme's goal, coding structure, programming logic and the relevant attributes of bug. Information retrieval (IR) based bug localization is a retrieval task, where bug reports and source files represent the queries and documents, respectively. In this paper, we propose BugCatcher, a newly developed bug localization method based on multi-level re-ranking IR technique. We evaluate BugCatcher on three open source projects with approximately 3400 bugs. Our experiments show that multi-level reranking approach to bug localization is promising. Retrieval performance and accuracy of BugCatcher are better than current bug localization tools, and BugCatcher has the best Top N, Mean Average Precision (MAP) and Mean Reciprocal Rank (MRR) values for all datasets. © 2016 Wiley Publishing Ltd
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    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.
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    A novel collocation method based on residual error analysis for solving integro-differential equations using hybrid Dickson and Taylor polynomials
    (Penerbit Universiti Kebangsaan Malaysia, 2017) Kürkçü O.K.; Aslan E.; Sezer M.
    In this study, a novel matrix method based on collocation points is proposed to solve some linear and nonlinear integrodifferential equations with variable coefficients under the mixed conditions. The solutions are obtained by means of Dickson and Taylor polynomials. The presented method transforms the equation and its conditions into matrix equations which comply with a system of linear algebraic equations with unknown Dickson coefficients, via collocation points in a finite interval. While solving the matrix equation, the Dickson coefficients and the polynomial approximation are obtained. Besides, the residual error analysis for our method is presented and illustrative examples are given to demonstrate the validity and applicability of the method.
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    A numerical method for solving some model problems arising in science and convergence analysis based on residual function
    (Elsevier B.V., 2017) Kürkçü Ö.K.; Aslan E.; Sezer M.
    In this study, we solve some widely-used model problems consisting of linear, nonlinear differential and integral equations, employing Dickson polynomials with the parameter-α and the collocation points for an efficient matrix method. The convergence of a Dickson polynomial solution of the model problem is investigated by means of the residual function. We encode useful computer programs for model problems, in order to obtain the precise Dickson polynomial solutions. These solutions are plotted along with the exact solutions in figures and the numerical results are compared with other well-known methods in tables. © 2017 IMACS
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    Edge harmonic index of carbon nanocones and an algorithm
    (Bulgarian Academy of Sciences, 2018) Aslan E.; Kürkçü O.K.
    Edge harmonic index He(G) of the (chemical) graph G is based on the end-vertex degrees of edges of the line graph L(G). In this paper, the generalized formula and an algorithm (pseudocode) are given for edge harmonic index. The aim of this paper is to develop edge harmonic index for generalized carbon nanocones. © 2018 Bulgarian Academy of Sciences, Union of Chemists in Bulgaria.
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    A Numerical Approach Technique for Solving Generalized Delay Integro-Differential Equations with Functional Bounds by Means of Dickson Polynomials
    (World Scientific Publishing Co. Pte Ltd, 2018) Kürkçü O.K.; Aslan E.; Sezer M.; Ilhan O.
    In this study, we have considered the linear classes of differential-(difference), integro-differential-(difference) and integral equations by constituting a generalized form, which contains proportional delay, difference, differentiable difference or delay. To solve the generalized form numerically, we use the efficient matrix technique based on Dickson polynomials with the parameter-α along with the collocation points. We also encode the useful computer program for susceptibility of the technique. The residual error analysis is implemented by using the residual function. The consistency of the technique is analyzed. Also, the numerical results illustrated in tables and figures are compared. © 2018 World Scientific Publishing Company.
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    A comparison between edge neighbor rupture degree and edge scattering number in graphs
    (World Scientific Publishing Co. Pte Ltd, 2018) Kürkçü Ö.K.; Aslan E.
    The vulnerability measure of a graph or a network depends on robustness of the remained graph, after being exposed to any intervention or attack. In this paper, we consider two edge vulnerability parameters that are the edge neighbor rupture degree and the edge scattering number. The values of these parameters of some specific graphs and their graph operations are calculated. Thus, we analyze and compare which parameter is distinctive for the different type of graphs by using tables. © 2018 World Scientific Publishing Company.
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    An investigation on the seasonal variations of the biomarkers of oxidative stress response and their correlations to Polonium-210 in mussel (Mytilus galloprovincialis) and common sole (Solea solea) from İzmir Bay, Turkey
    (Elsevier Ltd, 2018) Aslan E.; Uğur Görgün A.; Katalay S.; Filizok I.; Becerik S.; Aydemir T.
    It is well known that the marine organisms are used as biological indicators for environmental pollution studies. Among these studies, the research on oxidative stress has been increasing in recent years. In this study, mussels (Mytilus galloprovincialis) and fish (Solea solea) samples were collected seasonally from İnciraltı İzmir, Turkey. This station was in an area where fishing is carried out for human consumption. The relationship between 210Po and oxidative stress markers (lipid peroxidation (LPO), H2O2 and proline) was investigated in the mussel tissue (digestive gland, gills) and fish tissue (liver, gills) samples. The present study indicated that H2O2 accumulated with increasing 210Po concentration in mussel samples. Statistically significant correlation were found between H2O2 and 210Po and LPO and proline in mussel samples. This correlation between LPO and proline can be attributed to common environmental parameters (other than 210Po) affecting expression of both LPO and proline levels. There was not a significant correlation between 210Po and LPO levels. Similarly, a significant correlation was not found between 210Po and proline. © 2018 Elsevier Ltd
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    The average binding number of graphs
    (Science Society of Thailand under Royal Patronage, 2019) Aslan E.
    The binding number is a measure of the vulnerability of a graph. We investigate a refinement that involves the average of this parameter. Like the binding number itself, the average binding number bindav(G) of G measures the vulnerability of a graph, which is more sensitive. In this study, some bounds of the average binding number of some special graphs are obtained. Furthermore some results about the average binding number of graphs obtained from graph operations are also provided. © 2018 Science Society of Thailand under Royal Patronage. All rights reserved.