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Academic literature on the topic 'Grid graph'

Author: Grafiati

Published: 4 June 2021

Last updated: 20 June 2025

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Journal articles on the topic "Grid graph"

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V J Kaneria, H P Chudasama, and P P Andharia. "Absolute Mean Graceful Labeling in Path Union of Various Graphs." Mathematical Journal of Interdisciplinary Sciences 7, no. 1 (2018): 51–56. http://dx.doi.org/10.15415/mjis.2018.71008.

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Present paper aims to focus on absolute mean graceful labeling in path union of various graphs. We proved path union of graphs like tree, path Pn, cycle Cn, complete bipartite graph Km, n, grid graph PM × Pn, step grid graph Stn and double step grid graph DStn are absolute mean graceful graphs.

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Zamfirescu, Christina, and Tudor Zamfirescu. "Hamiltonicity of Topological Grid Graphs." JUCS - Journal of Universal Computer Science 13, no. (11) (2007): 1791–800. https://doi.org/10.3217/jucs-013-11-1791.

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In this paper we study connectivity and hamiltonicity properties of the topological grid graphs, which are a natural type of planar graphs associated with finite subgraphs of the usual square lattice graph of the plane. The main results are as follows. The shortness coefficient of the family of all topological grid graphs is at most 16/17. Every 3-connected topological grid graph is hamiltonian.

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Kor, Yashar, Liang Tan, Petr Musilek, and Marek Z. Reformat. "Integrating Knowledge Graphs into Distribution Grid Decision Support Systems." Future Internet 16, no. 1 (2023): 2. http://dx.doi.org/10.3390/fi16010002.

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Distribution grids are complex networks containing multiple pieces of equipment. These components are interconnected, and each of them is described by various attributes. A knowledge graph is an interesting data format that represents pieces of information as nodes and relations between the pieces as edges. In this paper, we describe the proposed vocabulary used to build a distribution system knowledge graph. We identify the concepts used in such graphs and a set of relations to represent links between concepts. Both provide a semantically rich representation of a system. Additionally, we offer a few illustrative examples of how a distributed system knowledge graph can be utilized to gain more insight into the operations of the grid. We show a simplified analysis of how outages can influence customers based on their locations and how adding DERs can influence/change it. These demonstrative use cases show that the graph-based representation of a distribution grid allows for integrating information of different types and how such a repository can be efficiently utilized. Based on the experiments with distribution system knowledge graphs presented in this article, we postulate that graph-based representation enables a novel way of storing information about power grids and facilitates interactive methods for their visualization and analysis.

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Hutson, Kevin R., and Stephen T. Hedetniemi. "Efficient Domination in Grid Graphs." Journal of Combinatorial Mathematics and Combinatorial Computing 122, no. 1 (2024): 325–42. http://dx.doi.org/10.61091/jcmcc122-27.

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Let G = ( V , E ) be a graph. A subset S ⊆ V of vertices is an \textit{efficient dominating set} if every vertex v ∈ V is adjacent to exactly one vertex in S , where a vertex u ∈ S is considered to be adjacent to itself. Efficient domination is highly desirable in many real-world applications, and yet, in general, graphs are often not efficient. It is of value, therefore, to determine optimum ways in which inefficient graphs can be changed in order to make them efficient. It is well known, for example, that almost no m × n grid graphs have efficient dominating sets. In this paper, we consider the minimum number of vertices that can be removed from an m × n grid graph so that the remaining graph has an efficient dominating set.

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Cyman, Joanna, and Joanna Raczek. "Application of Doubly Connected Dominating Sets to Safe Rectangular Smart Grids." Energies 15, no. 9 (2022): 2969. http://dx.doi.org/10.3390/en15092969.

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Smart grids, together with the Internet of Things, are considered to be the future of the electric energy world. This is possible through a two-way communication between nodes of the grids and computer processing. It is necessary that the communication is easy and safe, and the distance between a point of demand and supply is short, to reduce the electricity loss. All these requirements should be met at the lowest possible cost. In this paper, we study a two-dimensional rectangular grid graph which is considered to be a model of a smart grid; nodes of the graph represent points and devices of the smart grid, while links represent possible ways of communication and energy transfer. We consider the problem of choosing the lowest possible number of locations (nodes, points) of the grid which could serve as energy sources (or a source of different resources) to other nodes in such a way that we ensure reduction in electricity loss and provide safe communication and resistance to failures and increases in energy demand.Therefore, we study minimum doubly connected dominating sets in grid graphs. We show that the proposed solutions are the best possible in terms of the number of source points for the case of narrow grid graphs and we give upper and lower bounds for the case of wide grid graphs.

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Smirnov, Alexander Valeryevich. "Two-Step Colouring of Grid Graphs of Different Types." Modeling and Analysis of Information Systems 29, no. 3 (2022): 166–80. http://dx.doi.org/10.18255/1818-1015-2022-3-166-180.

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In this article, we consider the NP-hard problem of the two-step colouring of a graph. It is required to colour the graph in a given number of colours in a way, when no pair of vertices has the same colour, if these vertices are at a distance of 1 or 2 between each other. The optimum two-step colouring is one that uses the minimum possible number of colours.The two-step colouring problem is studied in application to grid graphs. We consider four types of grids: triangular, square, hexagonal, and octogonal. We show that the optimum two-step colouring of hexagonal and octogonal grid graphs requires 4 colours in the general case. We formulate the polynomial algorithms for such a colouring. A square grid graph with the maximum vertex degree equal to 3 requires 4 or 5 colours for a two-step colouring. In the paper, we suggest the backtracking algorithm for this case. Also, we present the algorithm, which works in linear time relative to the number of vertices, for the two-step colouring in 7 colours of a triangular grid graph and show that this colouring is always correct. If the maximum vertex degree equals 6, the solution is optimum.

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Kaneria, V. J., H. M. Makadia, and R. V. Viradia. "Graceful Labeling for Disconnected Grid Related Graphs." Bulletin of Mathematical Sciences and Applications 11 (February 2015): 6–11. http://dx.doi.org/10.18052/www.scipress.com/bmsa.11.6.

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In this paper we have proved that union of three grid graphs, U3l=1(Pnl×Pml)and union of finite copies of a grid graph (Pn×Pm)are graceful. We have also given two graceful labeling functions to the grid graph (Pn×Pm).

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W., K. M. Indunil, N. Kaluarachchi K., and C. G. Perera A. "k - Odd Prime Labeling of m×n Grid Graphs." Iconic Research and Engineering Journals 6, no. 6 (2022): 7. https://doi.org/10.5281/zenodo.7439763.

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Graph labeling can be mentioned as one of the most prominent research areas in graph theory and the history of graph labeling can be traced back to the 1960s as well. There is a  quite number of graph labeling techniques such as graceful labeling, radio labeling, antimagic labeling, prime labeling, and lucky labeling. There are various subtypes of prime labeling including odd prime labeling, k- prime labeling, neighborhood prime labeling, and coprime labeling. In this study, we explore one of the prime labeling varieties called odd prime labeling. There is a well-known conjecture related to this area that all the prime graphs are odd prime graphs. There is a vast number of publications regarding prime labeling and odd prime labeling for different classes of graphs. Recent works on odd prime labeling investigate different types of snake graphs, complete graphs, triangular-type snake graphs, different types of ladder graphs, families of cycle-related and path-related graphs, etc. In this research work, we introduce the concept of k- odd prime labeling and obtain several k- odd prime graphs such as m×n grid graph and variations of it.

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Dr., Hamzeh Mujahed, and Benedek Nagy Dr. "Exact Formula Computing the Wiener Index on Rows of Unit Cells of the Diamond Cubic Grid Connected in a Row." Palestinian Journal of Technology and Applied Sciences (PJTA) 2, no. 1 (2019): 69–81. https://doi.org/10.5281/zenodo.2576339.

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The Wiener Index, the sum of distances between all pairs of vertices in a connected graph, is a graph invariant much studied in both mathematical and chemical literature.Topological graph indices are introduced as mathematical tools for molecule descriptions. Recently, they were computed not only for graphs representing molecules, but for other regular structured graphs including some 2 and 3 dimensional structures. The Carbon atoms in the diamond are arranged in a well defined structure. In this paper, the graph of this structure is analysed, especially, the connected part of a sequence of unit cells. The Wiener index, as the sum of the distances for every pair of atoms is computed, a closed formula depending only on the number of unit cells is proven.

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Dr., Hamzeh Mujahed, and Benedek Nagy Dr. "Exact Formula Computing the Wiener Index on Rows of Unit Cells of the Diamond Cubic Grid Connected in a Row." Palestinian Journal of Technology & Applied Sciences (PJTA), no. 2 (March 4, 2019): 69–81. https://doi.org/10.5281/zenodo.2582919.

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The Wiener Index, the sum of distances between all pairs of vertices in a connected graph, is a graph invariant much studied in both mathematical and chemical literature.Topological graph indices are introduced as mathematical tools for molecule descriptions. Recently, they were computed not only for graphs representing molecules, but for other regular structured graphs including some 2 and 3 dimensional structures. The Carbon atoms in the diamond are arranged in a well defined structure. In this paper, the graph of this structure is analysed, especially, the connected part of a sequence of unit cells. The Wiener index, as the sum of the distances for every pair of atoms is computed, a closed formula depending only on the number of unit cells is proven.

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Dissertations / Theses on the topic "Grid graph"

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Rocha, Mário. "The embedding of complete bipartite graphs onto grids with a minimum grid cutwidth." CSUSB ScholarWorks, 2003. https://scholarworks.lib.csusb.edu/etd-project/2311.

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Wojciechowska, Iwona. "Broadcasting in grid graphs." Morgantown, W. Va. : [West Virginia University Libraries], 1999. http://etd.wvu.edu/templates/showETD.cfm?recnum=877.

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Thesis (Ph. D.)--West Virginia University, 1999.<br>Title from document title page. Document formatted into pages; contains vii, 69 p. : ill. Includes abstract. Includes bibliographical references (p. 67-69).

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Wang, Jiaxin. "Various pushing methods on grid graphs." Morgantown, W. Va. : [West Virginia University Libraries], 1999. http://etd.wvu.edu/templates/showETD.cfm?recnum=839.

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Thesis (M.S.)--West Virginia University, 1999.<br>Title from document title page. Document formatted into pages; contains v, 39 p. : ill. (some col.) Includes abstract. Includes bibliographical references (p. 39).

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Sterling, Christopher Kent. "Liar's Domination in Grid Graphs." Digital Commons @ East Tennessee State University, 2012. https://dc.etsu.edu/etd/1415.

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As introduced by Slater in 2008, liar's domination provides a way of modeling protection devices where one may be faulty. Assume each vertex of a graph G is the possible location for an intruder such as a thief. A protection device at a vertex v is assumed to be able to detect the intruder at any vertex in its closed neighborhood N[v] and identify at which vertex in N[v] the intruder is located. A dominating set is required to identify any intruder's location in the graph G, and if any one device can fail to detect the intruder, then a double-dominating set is necessary. Stronger still, a liar's dominating set can identify an intruder's location even when any one device in the neighborhood of the intruder vertex can lie, that is, any one device in the neighborhood of the intruder vertex can misidentify any vertex in its closed neighborhood as the intruder location or fail to report an intruder in its closed neighborhood. In this thesis, we present the liar's domination number for the finite ladders, infinite ladder, and infinite P_3 x P_infty. We also give bounds for other grid graphs.

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Curro', Vincenzo. "The Roman Domination Problem on Grid Graphs." Doctoral thesis, Università di Catania, 2014. http://hdl.handle.net/10761/1561.

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Domination is a rapidly developing area of research in graph theory. This dissertation focuses on the Roman Domination Problem; it was introduced quite recently and has some interesting applications in real world problems such military strategies and wireless networking. Given a graph, a Roman Dominating Function is a function that labels the vertices of the graph with an integer between 0, 1, 2, satisfying the condition that every vertex labeled by 0 is adjacent to at least one vertex labeled by 2. The weight of a Roman Dominating Function is the sum of all the labels, and the minimum weight is called the Roman Domination Number. The Roman Domination Problem is to find such number and function. In this dissertation we study the Roman Domination Problem when restricted to the class of grid graphs, i.e. graphs that, when drawn on an Euclidean Plane, form a specific regular tiling. A review of well--known results is given, and new results are presented. We aimed to find an algorithm that can find an exact solution for all the grid graphs, and, to do so, we present some important results: we prove a better lower-bound and present an upper-bound on the Roman Domination Number which improves the previous one and, we conjecture, is the Roman Domination Number for many, if not all, grid graphs.

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Ho, Yiu Yu. "Global secure sets of trees and grid-like graphs." Doctoral diss., University of Central Florida, 2011. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/4922.

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However, as will be demonstrated in Chapter 1, a defensive alliance may not be able to properly defend itself when multiple members are under attack at the same time. The concept of secure sets is introduced in (BDH07) for exactly this purpose. The non-empty set S is a secure set if every subset Xsubset of]S, with the assistance of vertices in S, can successfully defend against simultaneous attacks coming from vertices outside of S. The exact definition of simultaneous attacks and how such attacks may be defended will be provided in Chapter 1. In (BDH07), the authors presented an interesting characterization for secure sets which resembles the definition of defensive alliances. A non-empty set S is a secure set if and only if for all] X subset of] S, vertical line]N (X) intersection] Svertical line] greater than or equal to] vertical line]N(X) - Svertical line] ((BDH07),Theorem 11). The cardinality of a minimum secure set is the security number of G, denoted s(G). A secure set S is a global secure set if it further satisfies N (S)= V. The cardinality of a minimum global secure set of G is the global security number of G, denoted gamma subscript s](G). In this work, we present results on secure sets and global secure sets. In particular, we treat the computational complexity of finding the security number of a graph, present algorithms and bounds for the global security numbers of trees, and present the exact values of the global security numbers of paths, cycles and their Cartesian products.; Let G = (V, E) be a graph and let S subset of] V be a subset of vertices. The set S is a defensive alliance if for all x element of] S, vertical line]N(x)intersection] Svertical line]greater than or equal to] vertical line]N(x) - Svertical line]. The concept of defensive alliances was introduced in (KHH04), primarily for the modeling of nations in times of war, where allied nations are in mutual agreement to join forces if anyone of them is attacked. For a vertex x in a defensive alliance, the number of neighbors of x inside the alliance, plus the vertex x, is at least the number of neighbors of x outside the alliance. In a graph model, the vertices of a graph represent nations and the edges represent country boundaries. Thus, if the nation corresponding to a vertex x is attacked by its neighbors outside the alliance, the attack can be thwarted by x with the assistance of its neighbors in the alliance. In a different subject matter, (FLG00) applies graph theory to model the world wide web, where vertices represent websites and edges represent links between websites. A web community is a subset of vertices of the web graph, such that every vertex in the community has at least as many neighbors in the set as it has outside. So, a web community C satisfies for all] x element of] C, vertical line]N(x) intersection] Cvertical line] greater than] vertical line]N(x) - Cvertical line]. These sets are very similar to defensive alliances. They are known as strong defensive alliances in the literature of alliances in graphs. Other areas of application for alliances and related topics include classification, data clustering, ecology, business and social networks. Consider the application of modeling nations in times of war introduced in the first paragraph. In a defensive alliance, any attack on a single member of the alliance can be successfully defended.<br>ID: 030423421; System requirements: World Wide Web browser and PDF reader.; Mode of access: World Wide Web.; Thesis (Ph.D.)--University of Central Florida, 2011.; Includes bibliographical references (p. 206-210).<br>Ph.D.<br>Doctorate<br>Electrical Engineering and Computer Science<br>Engineering and Computer Science

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Laine, Scott T. "The grid bracing problem and a generalization." Link to electronic thesis, 2006. http://www.wpi.edu/Pubs/ETD/Available/etd-050106-132458/.

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Thesis (M.S.)--Worcester Polytechnic Institute.<br>Keywords: Unit Grid bracing, Infinitesimal motion, Rigidity Matrix, Rigidity Theory, Bracing a Unit Grid with a Window. Includes bibliographical references (p.57).

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Raak, Fredrik. "Investigation of Power Grid Islanding Based on Nonlinear Koopman Modes." Thesis, KTH, Elektriska energisystem, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-136834.

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To view the electricity supply in our society as just sockets mountedin our walls with a constant voltage output is far from the truth. Inreality, the power system supplying the electricity or the grid, is themost complex man-made dynamical system there is. It demands severecontrol and safety measures to ensure a reliable supply of electric power.Throughout the world, incidents of widespread power grid failures havebeen continuously reported. The state where electricity delivery to customersis terminated by a disturbance is called a blackout. From a stateof seemingly stable operating conditions, the grid can fast derail intoan uncontrollable state due to cascading failures. Transmission linesbecome automatically disconnected due to power flow redirections andparts of the grid become isolated and islands are formed. An islandedsub-grid incapable of maintaining safe operation conditions experiencesa blackout. A widespread blackout is a rare, but an extremely costlyand hazardous event for society.During recent years, many methods to prevent these kinds of eventshave been suggested. Controlled islanding has been a commonly suggestedstrategy to save the entire grid or parts of the grid from a blackout.Controlled islanding is a strategy of emergency control of a powergrid, in which the grid is intentionally split into a set of islanded subgridsfor avoiding an entire collapse. The key point in the strategy is todetermine appropriate separation boundaries, i.e. the set of transmissionlines separating the grid into two or more isolated parts.The power grid exhibits highly nonlinear response in the case oflarge failures. Therefore, this thesis proposes a new controlled islandingmethod for power grids based on the nonlinear Koopman Mode Analysis(KMA). The KMA is a new analyzing technique of nonlinear dynamicsbased on the so-called Koopman operator. Based on sampled data followinga disturbance, KMA is used to identify suitable partitions of thegrid.The KMA-based islanding method is numerically investigated withtwo well-known test systems proposed by the Institute of Electrical andElectronics Engineers (IEEE). By simulations of controlled islanding inthe test system, it is demonstrated that the grid’s response following afault can be improved with the proposed method.The proposed method is compared to a method of partitioning powergrids based on spectral graph theory which captures the structural propertiesof a network. It is shown that the intrinsic structural propertiesof a grid characterized by spectral graph theory are also captured by theKMA. This is shown both by numerical simulations and a theoreticalanalysis.

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Anguelov, Bobby. "Video game pathfinding and improvements to discrete search on grid-based maps." Diss., University of Pretoria, 2011. http://hdl.handle.net/2263/22940.

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The most basic requirement for any computer controlled game agent in a video game is to be able to successfully navigate the game environment. Pathfinding is an essential component of any agent navigation system. Pathfinding is, at the simplest level, a search technique for finding a route between two points in an environment. The real-time multi-agent nature of video games places extremely tight constraints on the pathfinding problem. This study aims to provide the first complete review of the current state of video game pathfinding both in regards to the graph search algorithms employed as well as the implications of pathfinding within dynamic game environments. Furthermore this thesis presents novel work in the form of a domain specific search algorithm for use on grid-based game maps: the spatial grid A* algorithm which is shown to offer significant improvements over A* within the intended domain. Copyright<br>Dissertation (MSc)--University of Pretoria, 2011.<br>Computer Science<br>unrestricted

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Löffler, Andre [Verfasser], Alexander [Gutachter] Wolff, and Steven [Gutachter] Chaplick. "Constrained Graph Layouts: Vertices on the Outer Face and on the Integer Grid / Andre Löffler ; Gutachter: Alexander Wolff, Steven Chaplick." Würzburg : Würzburg University Press, 2021. http://d-nb.info/1225684897/34.

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Books on the topic "Grid graph"

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Press, John. Pixel Grid Graph Paper: 100 Sheets Graph Paper Pixel Grids. Independently Published, 2019.

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Press, Paisley Cat. Project Notes: Graph Grid. Independently Published, 2019.

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Grid and Graph It. Fearon Teacher Aids, 1987.

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XANADU, Crystal. Graph It!: 4x4 Graph Grid 150 Pages. Independently Published, 2021.

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Notebooks, Style. Graph Paper Notebook: Grid Paper Journal - Grid Paper College Notebook - Graph Notebook. Independently Published, 2020.

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Notebooks, Style. Grid Notebook: Composition Graph Paper Notebook Grid / Graph Paper Journal - Grid Paper College Notebook 120 Pages. Independently Published, 2020.

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Ajguernoun, Said. Math graph paper: 1cm size graph paper grid. Independently Published, 2019.

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Pitzer, Dawnee. Graph Paper: Blank 1/2 Grid Graph Paper. Independently Published, 2021.

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Vero, Anima. Graph Paper Notebook: Grid Notebook. Independently Published, 2020.

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Ideabook: Graph Paper Grid Workbook. Independently Published, 2021.

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Book chapters on the topic "Grid graph"

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Pach, János, Torsten Thiele, and Géza Tóth. "Three-dimensional grid drawings of graphs." In Graph Drawing. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-63938-1_49.

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Balko, Martin. "Grid Drawings and the Chromatic Number." In Graph Drawing. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36763-2_28.

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Bachmaier, Christian, Franz J. Brandenburg, Wolfgang Brunner, Andreas Hofmeier, Marco Matzeder, and Thomas Unfried. "Tree Drawings on the Hexagonal Grid." In Graph Drawing. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00219-9_36.

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Eades, Peter, and Qing-Wen Feng. "Drawing clustered graphs on an orthogonal grid." In Graph Drawing. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-63938-1_58.

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He, Xin. "Grid embedding of 4-connected plane graphs." In Graph Drawing. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0021812.

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Aziza, Shabnam, and Therese Biedl. "Hexagonal Grid Drawings: Algorithms and Lower Bounds." In Graph Drawing. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-540-31843-9_3.

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Miura, Kazuyuki, Shin-ichi Nakano, and Takao Nishizeki. "Grid Drawings of Four-Connected Plane Graphs." In Graph Drawing. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-46648-7_15.

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Dujmović, Vida, and David R. Wood. "Three-Dimensional Grid Drawings with Sub-quadratic Volume." In Graph Drawing. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24595-7_18.

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Barrière, Lali, and Clemens Huemer. "4-Labelings and Grid Embeddings of Plane Quadrangulations." In Graph Drawing. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11805-0_41.

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Kratochvíl, Jan, and Teresa Przytycka. "Grid intersection and box intersection graphs on surfaces." In Graph Drawing. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0021820.

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Conference papers on the topic "Grid graph"

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Martin, Ioana Ramona, Tudor Cioara, Gabriel Ioan Arcas, Ionut Anghel, and Massimo Bertoncini. "Knowledge Graph Model for Computing Continuum Over Smart Grid." In 2024 15th International Conference on Information, Intelligence, Systems & Applications (IISA). IEEE, 2024. https://doi.org/10.1109/iisa62523.2024.10786635.

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Ni, Zhe, Xiaoxin Deng, Cong Tai, et al. "GRID: Scene-Graph-based Instruction-driven Robotic Task Planning." In 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2024. https://doi.org/10.1109/iros58592.2024.10801291.

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Li, Bo, Tianyou Zhu, Junjian Liu, Hongwei Lv, Zhenyu Chen, and Senda Zhang. "Knowledge Graph QA for Weakly Supervised Power Grid Signals." In 2023 International Conference on Information Processing and Network Provisioning (ICIPNP). IEEE, 2023. https://doi.org/10.1109/icipnp62754.2023.00057.

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Zhang, Yadong, Pranav M. Karve, and Sankaran Mahadevan. "Power grid operational risk assessment using graph neural network surrogates." In 2024 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2024. http://dx.doi.org/10.1109/pesgm51994.2024.10688788.

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Dai, Zhen, Jun Tan, Wei Zhang, Xinglang Xie, Xueqing Song, and Yuanfa Deng. "Novel Graph-based Transient Analysis Method for Bulk Power System." In 2024 6th International Conference on Energy, Power and Grid (ICEPG). IEEE, 2024. https://doi.org/10.1109/icepg63230.2024.10775541.

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Pourmoradi, Nazanin, Sasan Azad, and Mohammad Taghi Ameli. "A Transfer Learning Based Graph Convolutional Network for Intelligent Load Shedding in Modern Power Systems for Unknown Faults." In 2024 14th Smart Grid Conference (SGC). IEEE, 2024. https://doi.org/10.1109/sgc64640.2024.10983018.

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Indunil, W. K. M., та A. A. I. Perera. "𝒌 – Graceful Labeling of Triangular Type Grid Graphs 𝑫𝒏(𝑷𝒎) and 𝑳 – Vertex Union of 𝑫𝒏(𝑷𝒎)". У SLIIT 2nd International Conference on Engineering and Technology. SLIIT, 2023. http://dx.doi.org/10.54389/ilio4846.

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Graph labeling is one of the most popular research topics in the field of graph theory. Prime labeling, antimagic labeling, radio labeling, graceful labeling, lucky labeling, and incidence labeling are some of the labeling techniques. Among the above-mentioned techniques, graceful labeling is one of the most engaging graph labeling techniques with a vast amount of real-world applications. Over the past few decades, plenty of studies have been conducted on this area in various dimensions. Grid graphs are very much useful in applications of circuit theory, communication networks, and transportation networks. However, in the literature, there are not many research papers on the graceful labeling of grid graphs except a few on odd graceful labeling. In our work, we prove that triangular-type grid graphs, 𝐷𝑛(𝑃𝑚) and 𝐿 – vertex union of 𝐷𝑛(𝑃𝑚) admit 𝑘 – general graceful labeling and 𝑘 – even and 𝑘 – odd graceful labeling. Further, we introduce combinatorial proofs for them as well. KEYWORDS: 𝒌 – even graceful labeling, 𝒌 – graceful labeling, 𝒌 – odd graceful labeling, triangular type grid graph.

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Zhang, Zaixi, Qi Liu, Zhenya Huang, et al. "GraphMI: Extracting Private Graph Data from Graph Neural Networks." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/516.

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As machine learning becomes more widely used for critical applications, the need to study its implications in privacy becomes urgent. Given access to the target model and auxiliary information, model inversion attack aims to infer sensitive features of the training dataset, which leads to great privacy concerns. Despite its success in the grid domain, directly applying model inversion techniques on non grid domains such as graph achieves poor attack performance due to the difficulty to fully exploit the intrinsic properties of graphs and attributes of graph nodes used in GNN models. To bridge this gap, we present Graph Model Inversion attack, which aims to infer edges of the training graph by inverting Graph Neural Networks, one of the most popular graph analysis tools. Specifically, the projected gradient module in our method can tackle the discreteness of graph edges while preserving the sparsity and smoothness of graph features. Moreover, a well designed graph autoencoder module can efficiently exploit graph topology, node attributes, and target model parameters. With the proposed method, we study the connection between model inversion risk and edge influence and show that edges with greater influence are more likely to be recovered. Extensive experiments over several public datasets demonstrate the effectiveness of our method. We also show that differential privacy in its canonical form can hardly defend our attack while preserving decent utility.

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Luo, Gongxu, Jianxin Li, Hao Peng, et al. "Graph Entropy Guided Node Embedding Dimension Selection for Graph Neural Networks." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/381.

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Graph representation learning has achieved great success in many areas, including e-commerce, chemistry, biology, etc. However, the fundamental problem of choosing the appropriate dimension of node embedding for a given graph still remains unsolved. The commonly used strategies for Node Embedding Dimension Selection (NEDS) based on grid search or empirical knowledge suffer from heavy computation and poor model performance. In this paper, we revisit NEDS from the perspective of minimum entropy principle. Subsequently, we propose a novel Minimum Graph Entropy (MinGE) algorithm for NEDS with graph data. To be specific, MinGE considers both feature entropy and structure entropy on graphs, which are carefully designed according to the characteristics of the rich information in them. The feature entropy, which assumes the embeddings of adjacent nodes to be more similar, connects node features and link topology on graphs. The structure entropy takes the normalized degree as basic unit to further measure the higher-order structure of graphs. Based on them, we design MinGE to directly calculate the ideal node embedding dimension for any graph. Finally, comprehensive experiments with popular Graph Neural Networks (GNNs) on benchmark datasets demonstrate the effectiveness and generalizability of our proposed MinGE.

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Rappoport, A., and I. Kurochkin. "THE GRAPH DIAMETER OF A DISTRIBUTED SYSTEM WITH A GIVEN DOMINANT SET." In 9th International Conference "Distributed Computing and Grid Technologies in Science and Education". Crossref, 2021. http://dx.doi.org/10.54546/mlit.2021.63.14.001.

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In this work consider a distributed computing system in which the control functions are dispersed inseveral dominant nodes that are directly connected to all the others. This configuration reduces thevulnerability of the entire network, since the failure of a single control element immediately disruptsits operation. On the other hand, the large length of the maximum shortest chain (diameter) increasesthe data transfer time, which is bad for the functioning of the entire system. The connection of themaximum shortest chain of a distributed network graph with the size of a certain dominant set isinvestigated. The structure of a graph with a maximum diameter on the set of all graphs with a givendominant set is presented, a diametrical chain is constructed, and the value of the extreme diameter isestimated. Based on this construction, it is possible to generate various network graphs with a givendominant set and a diameter that takes certain values. A number of operations are proposed thatchange the edge set of the original graph. As a result, this method provides a way to construct graphstructures with given metric characteristics.

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Reports on the topic "Grid graph"

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Ponce, Colin, and Panayot S. Vassilevski. Solving Graph Laplacian Systems Through Recursive Bisections and Two-Grid Preconditioning. Office of Scientific and Technical Information (OSTI), 2016. http://dx.doi.org/10.2172/1240975.

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Li, Wenting. Robust Fault Location in Power Grids through Graph Learning at Low Label Rates. Office of Scientific and Technical Information (OSTI), 2021. http://dx.doi.org/10.2172/1768426.

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Beck, D. M., M. J. Scott, S. F. Shindle, et al. Hanford Area 1990 population and 50-year projections. [Appendix contains computer programming for population projections and graphs showing them by grid areas]. Office of Scientific and Technical Information (OSTI), 1991. http://dx.doi.org/10.2172/5070450.

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Trepp, Megan, Gail R. Nonnecke, Paul A. Domoto, and Dennis N. Portz. Maturation of Recently Released Cold Hardy Wine Grap Cultivars in Iowa: Corot noir, Frontenac Gris, La Crescent, Marquette, and Noiret. Iowa State University, Digital Repository, 2009. http://dx.doi.org/10.31274/farmprogressreports-180814-2133.

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Reisch, Bruce, Pinhas Spiegel-Roy, Norman Weeden, Gozal Ben-Hayyim, and Jacques Beckmann. Genetic Analysis in vitis Using Molecular Markers. United States Department of Agriculture, 1995. http://dx.doi.org/10.32747/1995.7613014.bard.

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Genetic analysis and mapping in grapes has been difficult because of the long generation period and paucity of genetic markers. In the present work, chromosome linkage maps were developed with RAPD, RFLP and isozyme loci in interspecific hybrid cultivars, and RAPD markers were produced in a V. vinifera population. In three cultivars, there were 19 linkage groups as expected for a species with 38 somatic chromosomes. These maps were used to locate chromosome regions with linkages to important genes, including those influencing powdery mildew and botrytis bunch rot resistance; flower sex; and berry shape. In V. vinifera, the occurrence of specific markers was correlated with seedlessness, muscat flavor and fruit color. Polymorphic RAPD bands included single copy as well as repetitive DNA. Mapping procedures were improved by optimizing PCR parameters with grape DNA; by the development of an efficient DNA extraction protocol; and with the use of long (17- to 24-mer) primers which amplify more polymorphic loci per primer. DNA fingerprint analysis with RAPD markers indicated that vinifera cultivars could be separated readily with RAPD profiles. Pinot gris, thought to be a sort of Pinot noir, differed by 12 bands from Pinot noir. This suggests that while Pinot gris may be related to Pinot noir, it is not likely to be a clone. The techniques developed in this project are now being further refined to use marker-assisted selection in breeding programs for the early selection of elite seedlings. Furthermore, the stage has been set for future attempts to clone genes from grapes based upon map locations.

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