• Journal of applied mathematics & informatics
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• v.42 no.5
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• pp.1137-1144
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• 2024

We are concerned with the T-Graphs, denoted by G_T, which are graphs defined based on the Topological structure of the given set. Precisely, for a given topology T on a set X, a T-Graph G = (V,E) is an undirected graph. In this graph, the vertex set V is P(X) and the edge set E consists of all unordered pairs of nodes u and v in V, denoted by (u, v). The pair of nodes satisfies the condition that u ∈ T and u^c ∩ v ∈ T, where u^c is the complement of the subset u of X. The primary objective of this paper is threefold: (i) Find that the number of triangles (ii) we intend to establish that the number of rectangles and (iii) the number of Hamiltonian cycles and Eulerian closed trials in a graph G_T.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.1
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• pp.1-6
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• 2002

David Gavid [3] proved that in many familiar cases the upper semi-finite topology on the set of closed subsets of a space is the largest topology making the coincidence function continuous, when the collection of functions is given the graph topology. Considering G-spaces and taking the coincidence set to consist of points where orbits coincidence, we obtain G-version of many of his results.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.31 no.5
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• pp.411-419
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• 2013

Research on developing algorithms for building modeling such as extracting outlines of the buildings and segmenting patches of the roofs using aerial images or LiDAR data are active. However, utilizing information from the building model is not well implemented yet. This study aims to propose a scheme for search identical or similar shape of buildings by utilizing graph topology pattern matching under the assumptions: (1) Buildings were modeled beforehand using imagery or LiDAR data, or (2) 3D building data from digital maps are available. Side walls, segmented roofs and footprints were represented as nodes, and relationships among the nodes were defined using graph topology. Topology graph database was generated and pattern matching was performed with buildings of various shapes. The results show that efficiency of the proposed method in terms of reliability of matching and database structure. In addition, flexibility in the search was achieved by altering conditions for the pattern matching. Furthermore, topology graph representation could be used as scale and rotation invariant shape descriptor.

• Journal of Korea Multimedia Society
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• v.5 no.1
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• pp.114-119
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• 2002

Realtime assignment of railways is an important component in the railway control systems. To solve this problem, we must exactly represent the track topology. Graph is a proper data structure for representing general network topologies, but not Proper for track topologies. In this paper, we define a new data structure, railway graph, which can exactly represent topologies of railway networks. And we describe a path search algorithm in the defined railway graph, and a top-down approach for designing railway network by the Proposed graph.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.2D
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• pp.171-179
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• 2010

The purpose of the present study is to suggest composing the graph topology of sketch drawing element and the recognition of the shape pattern for the earthwork quantity calculation. The algorithm which can extract the topology element such as vertex, edge, face and establish the relation between each topology was developed. The model which can define earthwork graph and recognize the shape pattern of earthwork was presented. As a result of the study, the shape pattern of earthwork that can't be calculated by existing earthwork calculation program could be recognized as expanding this model. The earthwork shape recognition automation using the graph topology model can be applied to the automation for the earthwork quantity estimation.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.108-113
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• 2005

This paper suggests a control method for an efficient topology/parameter evolution in a bond graph-based GP design framework that automatically synthesizes designs for multi-domain, lumped parameter dynamic systems. We adopt a hierarchical breeding control mechanism with fitness-level-dependent differences to obtain better balancing of topology/parameter search - biased toward topological changes at low fitness levels, and toward parameter changes at high fitness levels. As a testbed for this approach in bond graph synthesis, an eigenvalue assignment problem, which is to find bond graph models exhibiting minimal distance errors from target sets of eigenvalues, was tested and showed improved performance for various sets of eigenvalues.

• IEMEK Journal of Embedded Systems and Applications
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• v.14 no.4
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• pp.219-226
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• 2019

One of the most widely studied protocols for tactical ad-hoc networks is Optimized Link State Routing Protocol (OLSR). As for OLSR research, most research work focus on reducing control traffic overhead and choosing relay point. In addition, because OLSR is mostly dependent on link detection and propagation, dynamic Hello timer become research challenges. However, different timer interval causes imbalance of link validity time by affecting link lifetime. To solve this problem, we propose a weighted topology graph model for constructing a robust network topology based on the link validity time. In order to calculate the link validity time, we use control message timer, which is set for each node. The simulation results show that the proposed mechanism is able to achieve high end-to-end reliability and low end-to-end delay in small networks.

• Proceedings of the KIEE Conference
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• 2000.11b
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• pp.389-391
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• 2000

A representation technique of a given track topology is required by many software applications in railway technology such as signalling system simulator. To achieve these, the concept of double vertex graph architecture is proposed. These are composed of pairs of vertices and node between the single vertices. Double vertex graph architecture can be understood as a extension of classical graphs. In developed railway signalling simulation software, it is shown that track topology can be represented by proposed algorithm in a efficient way. Especially it makes sure that these are suitable technique for representing and implementing of switch, routes which can be introduced some mistake in classical graph algorithm.

• Honam Mathematical Journal
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• v.27 no.1
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• pp.115-129
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• 2005

In this paper, we give a digital graph-theoretical approach of the study of digital images with relation to a simplicial complex. Thus, a digital graph $G_k$ with some k-adjacency in ${\mathbb{Z}}^n$ can be recognized by the simplicial complex spanned by $G_k$. Moreover, we demonstrate that a graphically $(k_0,\;k_1)$-continuous map $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}}^{n_1}$ can be converted into the simplicial map $S(f):S(G_{k_0}){\rightarrow}S(G_{k_1})$ with relation to combinatorial topology. Finally, if $G_{k_0}$ is not $(k_0,\;3^{n_0}-1)$-homotopy equivalent to $SC^{n_0,4}_{3^{n_0}-1}$, a graphically $(k_0,\;k_1)$-continuous map (respectively a graphically $(k_0,\;k_1)$-isomorphisim) $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}^{n_1}$ induces the group homomorphism (respectively the group isomorphisim) $S(f)_*:{\pi}_1(S(G_{k_0}),\;v_0){\rightarrow}{\pi}_1(S(G_{k_1}),\;f(v_0))$ in algebraic topology.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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• pp.185-188
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• 2005

This paper suggests a control method for efficient topology/parameter evolution in a bond-graph-based GP design framework that automatically synthesizes designs for multi-domain, lumped parameter dynamic systems, We adopt a hierarchical breeding control mechanism with fitness-level-dependent differences to obtain better balancing of topology/parameter search - biased toward topological changes at low fitness levels, and toward parameter changes at high fitness levels. As a testbed for this approach, an eigenvalue assignment problem, which is to find bond graph models exhibiting minimal distance errors from target sets of eigenvalues, was tested and showed improved performance for various sets of eigenvalues.