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Author

Darko Dimitrov

Other affiliations: Free University of Berlin
Bio: Darko Dimitrov is an academic researcher from HTW Berlin - University of Applied Sciences. The author has contributed to research in topics: Topological index & Degree (graph theory). The author has an hindex of 20, co-authored 59 publications receiving 1224 citations. Previous affiliations of Darko Dimitrov include Free University of Berlin.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors studied the fourth multiplicative atom-bond connectivity indices of some special molecular structures which commonly appeared in the compound of nanomaterials, and their specific expressions are given.

168 citations

Journal ArticleDOI
TL;DR: It is determined that G is a fractional -critical deleted graph and the independent set neighborhood union condition for a graph to be fractional ID- (g,f,m) -deleted is raised.
Abstract: The problem of data transmission in communication network can betransformed into the problem of fractional factor existing in graph theory. Inrecent years, the data transmission problem in the specificnetwork conditions has received a great deal of attention, and itraises new demands to the corresponding mathematical model. Underthis background, many advanced results are presented on fractionalcritical deleted graphs and fractional ID deleted graphs. In thispaper, we determine that $G$ is a fractional \begin{document}$ (g,f,n',m) $\end{document} -critical deleted graph if \begin{document}$ δ(G)≥\frac{b^{2}(i-1)}{a}+n'+2m $\end{document} , \begin{document}$ n>\frac{(a+b)(i(a+b)+2m-2)+bn'}{a} $\end{document} , and \begin{document}$|N_{G}(x_{1})\cup N_{G}(x_{2})\cup···\cup N_{G}(x_{i})|≥\frac{b(n+n')}{a+b}$ \end{document} for any independent subset \begin{document}$ \{x_{1},x_{2},..., x_{i}\} $\end{document} of \begin{document}$ V(G) $\end{document} . Furthermore, the independent set neighborhood union condition for a graph to be fractional ID- \begin{document}$ (g,f,m) $\end{document} -deleted is raised. Some examples will be manifested to show the sharpness of independent set neighborhood union conditions.

104 citations

Journal ArticleDOI
TL;DR: The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants, which are found in a vast variety of chemical applications.
Abstract: The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants, which are found in a vast variety of chemical applications. For a simple graph $G$ , it is defined as $ABC(G)=\sum _{uv \in E(G)} ({({d(u)+d(v)-2})/({d(u) d(v)})})^{1/2}$ , where $d(v)$ denotes the degree of a vertex $v$ of $G$ . Recently in [17] graphs with $n$ vertices, $2n-4$ and $2n-3$ edges, and maximum $ABC$ index were characterized. Here, we consider the next, more complex case, and characterize the graphs with $n$ vertices, $2n-2$ edges, and maximum $ABC$ index.

97 citations

Journal ArticleDOI
TL;DR: All graphs with maximal total irregularity are determined and it is shown that among all trees of the same order the star has the maximaltotal irregularity.
Abstract: is defined as irrt(G) = 1 P u;v2V (G) jdG(u) dG(v)j; where dG(u) denotes the degree of a vertex u2 V (G). All graphs with maximal total irregularity are determined. It is also shown that among all trees of the same order the star has the maximal total irregularity.

68 citations

Posted Content
TL;DR: In this article, a new measure of irregularity of a simple undirected graph is introduced, called the total irregularity, which is defined as 1/2 √ √ sum √ u, v in V(G), where u is the degree of a vertex and v is a vertex.
Abstract: In this note a new measure of irregularity of a simple undirected graph $G$ is introduced. It is named the total irregularity of a graph and is defined as $\irr_t(G) = 1/2\sum_{u,v \in V(G)} |d_G(u)-d_G(v)|$, where $d_G(u)$ denotes the degree of a vertex $u \in V(G)$. The graphs with maximal total irregularity are determined. It is also shown that among all trees of same order the star graph has the maximal total irregularity.

64 citations


Cited by
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Journal ArticleDOI
TL;DR: The proposed slime mould algorithm has several new features with a unique mathematical model that uses adaptive weights to simulate the process of producing positive and negative feedback of the propagation wave of slime mould based on bio-oscillator to form the optimal path for connecting food with excellent exploratory ability and exploitation propensity.

1,443 citations

Journal ArticleDOI
TL;DR: The first powerful variant of the Harris hawks optimization (HHO) integrates chaos strategy, topological multi-population strategy, and differential evolution (DE) strategy and is compared with a range of other methods.

240 citations

Journal ArticleDOI
TL;DR: This paper presents novel loss functions for training convolutional neural network (CNN)-based segmentation methods with the goal of reducing HD directly, and suggests three loss functions that can be used for training to reduce HD.
Abstract: The Hausdorff Distance (HD) is widely used in evaluating medical image segmentation methods. However, the existing segmentation methods do not attempt to reduce HD directly. In this paper, we present novel loss functions for training convolutional neural network (CNN)-based segmentation methods with the goal of reducing HD directly. We propose three methods to estimate HD from the segmentation probability map produced by a CNN. One method makes use of the distance transform of the segmentation boundary. Another method is based on applying morphological erosion on the difference between the true and estimated segmentation maps. The third method works by applying circular/spherical convolution kernels of different radii on the segmentation probability maps. Based on these three methods for estimating HD, we suggest three loss functions that can be used for training to reduce HD. We use these loss functions to train CNNs for segmentation of the prostate, liver, and pancreas in ultrasound, magnetic resonance, and computed tomography images and compare the results with commonly-used loss functions. Our results show that the proposed loss functions can lead to approximately 18–45% reduction in HD without degrading other segmentation performance criteria such as the Dice similarity coefficient. The proposed loss functions can be used for training medical image segmentation methods in order to reduce the large segmentation errors.

238 citations

Journal ArticleDOI
TL;DR: A novel HHO called IHHO is proposed by embedding the salp swarm algorithm (SSA) into the original HHO to improve the search ability of the optimizer and expand the application fields and the experimental results reveal that the proposed I HHO has better accuracy rates over other compared wrapper FS methods.
Abstract: Feature selection is a required preprocess stage in most of the data mining tasks. This paper presents an improved Harris hawks optimization (HHO) to find high-quality solutions for global optimization and feature selection tasks. This method is an efficient optimizer inspired by the behaviors of Harris' hawks, which try to catch the rabbits. In some cases, the original version tends to stagnate to the local optimum solutions. Hence, a novel HHO called IHHO is proposed by embedding the salp swarm algorithm (SSA) into the original HHO to improve the search ability of the optimizer and expand the application fields. The update stage in the HHO optimizer, which is performed to update each hawk, is divided into three phases: adjusting population based on SSA to generate SSA-based population, generating hybrid individuals according to SSA-based individual and HHO-based individual, and updating search agent in the light of greedy selection and HHO’s mechanisms. A large group of experiments on many functions is carried out to investigate the efficacy of the proposed optimizer. Based on the overall results, the proposed IHHO can provide a faster convergence speed and maintain a better balance between exploration and exploitation. Moreover, according to the proposed continuous IHHO, a more stable binary IHHO is also constructed as a wrapper-based feature selection (FS) approach. We compare the resulting binary IHHO with other FS methods using well-known benchmark datasets provided by UCI. The experimental results reveal that the proposed IHHO has better accuracy rates over other compared wrapper FS methods. Overall research and analysis confirm the improvement in IHHO because of the suitable exploration capability of SSA.

229 citations

Journal ArticleDOI
TL;DR: HHO-based identifier provides high-quality solutions for parameter identification cases based on its coherent searching trends and is recommended as a competent and auxiliary technique for parameters estimation of photovoltaic models.

227 citations