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Automatic Diagram Layout
Jezný, Lukáš ; Chmelař, Petr (referee) ; Herout, Adam (advisor)
Automatic layouts for diagram drawing is described in this paper. Major methods, algorithms, metrics for automatic layouts are introduced in theretical part. Practical part of this work was developing algorithms for automatic layouts of organizational structures and business process model diagrams.
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Graphical Vizualization of Routing Algorithms
Pokorný, Martin ; Gajda, Zbyšek (referee) ; Jaroš, Jiří (advisor)
The aim of this bachelor's thesis is illustrate network topology, e.g . computers or processor, and communication in this network. The network can be displayed like a various topology, which is possible to manually modify. Position and interconnection of vertex is stored in delivered file. Second part of program is on displayed topology demonstrate collective communication between vertex. The kind of collective communication depend on selected routing algorithm, which is again stored in delivered file. Program output can be saved in the form of raster picture or XML document.
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Eberhard-Like Theorems
Šimečková, Zuzana ; Šámal, Robert (advisor) ; Fiala, Jiří (referee)
Define sequence (pk) = (p3,p4, . . . ) as numbers of k-sized faces - k-gons - of an embedding of a planar graph. A corollary to Euler's formula for planar graphs states that for cubic graphs ∑ k>=3 (6 − k)pk = 12 holds. Naturally, this leads us to explore the nature of p for which a corresponding cubic planar graph exists. Eberhard proved that if p satisfies the equality above then a cubic planar graph that corresponds to p except for the number of hexagons, exists. DeVos et al. show similar theorem, but instead of hexagon, both pentagons and heptagons can be added. In this thesis, we extend their result by using their proof strategy and designing a program to find graphs needed in such proof. We were able to prove that for every pair r,s ∈ N where s < 6 < r < 14 and r,s are coprime the following theorem holds: for each sequence of nonnegative integers satisfying ∑ k>=3 (6 − k)pk = 12 there are infinitely many cubic planar graphs corresponding to p except for the number of both r-gons and s-gons. 1
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Automatic Diagram Layout
Jezný, Lukáš ; Chmelař, Petr (referee) ; Herout, Adam (advisor)
Automatic layouts for diagram drawing is described in this paper. Major methods, algorithms, metrics for automatic layouts are introduced in theretical part. Practical part of this work was developing algorithms for automatic layouts of organizational structures and business process model diagrams.
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Eberhard-Like Theorems
Šimečková, Zuzana ; Šámal, Robert (advisor) ; Fiala, Jiří (referee)
Define sequence (pk) = (p3,p4, . . . ) as numbers of k-sized faces - k-gons - of an embedding of a planar graph. A corollary to Euler's formula for planar graphs states that for cubic graphs ∑ k>=3 (6 − k)pk = 12 holds. Naturally, this leads us to explore the nature of p for which a corresponding cubic planar graph exists. Eberhard proved that if p satisfies the equality above then a cubic planar graph that corresponds to p except for the number of hexagons, exists. DeVos et al. show similar theorem, but instead of hexagon, both pentagons and heptagons can be added. In this thesis, we extend their result by using their proof strategy and designing a program to find graphs needed in such proof. We were able to prove that for every pair r,s ∈ N where s < 6 < r < 14 and r,s are coprime the following theorem holds: for each sequence of nonnegative integers satisfying ∑ k>=3 (6 − k)pk = 12 there are infinitely many cubic planar graphs corresponding to p except for the number of both r-gons and s-gons. 1
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Drawing graphs on surfaces of small genus
Tomášek, Jan ; Dvořák, Zdeněk (advisor) ; Šámal, Robert (referee)
Although there are many algorithms for drawing graphs on arbitrary surfaces, surprisingly few of them have been practically implemented. This thesis designs a user-friendly graphical interface for drawing graphs and torus, which allows checking the results of algorithms. The program supports displaying the surfaces in the polygonal representation and in their 3-dimension embedding. Furthermore we survey the algorithms for drawing graphs on surfaces and discuss their implementability. We chose one of the algorithms and evaluate its performance. Powered by TCPDF (www.tcpdf.org)
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Graphical Vizualization of Routing Algorithms
Pokorný, Martin ; Gajda, Zbyšek (referee) ; Jaroš, Jiří (advisor)
The aim of this bachelor's thesis is illustrate network topology, e.g . computers or processor, and communication in this network. The network can be displayed like a various topology, which is possible to manually modify. Position and interconnection of vertex is stored in delivered file. Second part of program is on displayed topology demonstrate collective communication between vertex. The kind of collective communication depend on selected routing algorithm, which is again stored in delivered file. Program output can be saved in the form of raster picture or XML document.
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