Partition dimension of certain classes of series parallel graphs

Mohan, Chris Monica; Santhakumar, S.; Arockiaraj, Micheal; Liu, Jia‐Bao

doi:10.1016/j.tcs.2019.01.026

Cited by 16 publications

(8 citation statements)

References 17 publications

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“…In 1986, Canny took the lead in proposing the optimal stepped edge detection operator [5], which is the optimal result for continuous jump edge processing interfered by white noise [14]. Canny operator extraction effect of the projection image boundary is better, and it is closer to the real boundary contour.…”

Section: Data Processingmentioning

confidence: 99%

“…Szczykutowicz et al [4] proposed a proprietary deep learning image reconstruction method (DLIR) based on deep learning. Liu et al [5,6] considered the reconstruction of the point set of the graph, which also provided some inspiration for the innovation of image reconstruction methods. In edge monitoring, Asghari and Jalali [7] proposed to transform images by simulating the propagation of light through physical media with specific distorted diffraction characteristics, effectively revealing the transition of image intensity.…”

Section: Introductionmentioning

confidence: 99%

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Application of Image Reconstruction Based on Inverse Radon Transform in CT System Parameter Calibration and Imaging

et al. 2021

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According to the requirements of CT system parameter calibration and imaging, using OpenCV and MATLAB software, the reverse Radon transform and the Canny edge detection algorithm in the projection edge methods can determine the position and geometry of two different media in the square tray based on given data. Besides, it can apply and analyze the shape and the absorption rate of the specified point, the accuracy, and stability of the template calibration parameters by this way, which enables designing a new template and calibrating the new parameters.

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Section: Data Processingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Application of Image Reconstruction Based on Inverse Radon Transform in CT System Parameter Calibration and Imaging

et al. 2021

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“…Our methods, on the other hand, are able to be considered concise because of reducing some complicated calculations in comparison with many commonly used methods. One of the most important reasons for this is that we present these methods by taking into account structure features of the both treelike models throughout [22,23]. Meantime, we have determined the formula of geodesic distance on n-order subdivision tree models in [24].…”

Section: Conclusion and Problemmentioning

confidence: 99%

Exact solutions for geodesic distance on treelike models with some constraints

Luo¹,

Ma²,

Xu³

2019

Preprint

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Geodesic distance, commonly called shortest path length, has proved useful in a great variety of disciplines. It has been playing a significant role in search engine at present and so attracted considerable attention at the last few decades, particularly, almost all data structures and corresponding algorithms suitable to searching information generated based on treelike models. Hence, we, in this paper, study in detail geodesic distance on some treelike models which can be generated by three different types of operations, including first-order subdivision, (1, m)-star-fractal operation and m-vertex-operation. Compared to the most best used approaches for calculating geodesic distance on graphs, for instance, enumeration method and matrix multiplication, we take useful advantage of a novel method consisting in spirit of the concept of vertex cover in the language of graph theory and mapping. For each kind of treelike model addressed here, we certainly obtain an exact solution for its geodesic distance using our method. With the help of computer simulations, we confirm that the analytical results are in perfect agreement with simulations. In addition, we also report some intriguing structure properties on treelike models of two types among them. The one obeys exponential degree distribution seen in many complex networks, by contrast, the other possesses all but leaf vertices with identical degree and shows more homogeneous topological structure than the former. Besides that, the both have, in some sense, self-similar feature but instead the latter exhibits fractal property.

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“…In [11,12],; for any integers 𝑠 𝑖 ≥ 1 for each i, the generalized theta graph Θ(𝑠 1 , 𝑠 2 , … . , 𝑠 𝑙 ) is a graph consists of a pair of end vertices, say x and y, joined by 𝑙 internally disjoint paths of lengths 𝑠 𝑖 + 1 for each 𝑖 ∈…”

Section: Introductionmentioning

confidence: 99%

Distinguishing Number of the Generalized Theta Graph

Rahadi¹,

Baskoro²,

Saputro³

2022

Advances in Computer Science Research

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A generalized theta graph is a graph constructed from two distinct vertices by joining them with 𝑙 (>=3) internally disjoint paths of lengths greater than one. The distinguishing number 𝐷(𝐺) of a graph 𝐺 is the least integer 𝑑 such that 𝐺 has a vertex labelling with 𝑑 labels that is preserved only by a trivial automorphism. The partition dimension of a graph G is the least k such that V(G) can be k-partitioned such that the representations of all vertices are distinct with respect to that partition. In this paper, we establish a relation between the distinguishing number and the partition dimension of a graph. We also determine the distinguishing number for the generalized theta graph.

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Partition dimension of certain classes of series parallel graphs

Cited by 16 publications

References 17 publications

Application of Image Reconstruction Based on Inverse Radon Transform in CT System Parameter Calibration and Imaging

Application of Image Reconstruction Based on Inverse Radon Transform in CT System Parameter Calibration and Imaging

Exact solutions for geodesic distance on treelike models with some constraints

Distinguishing Number of the Generalized Theta Graph

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