Graphs and Matrices

摘要

Previous article Next article Graphs and MatricesFrank HararyFrank Hararyhttps://doi.org/10.1137/1009003PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] T. van Aardenne-Ehrenfest and , N. G. de Bruijn, Circuits and trees in oriented linear graphs, Simon Stevin, 28 (1951), 203–217 MR0047311 0044.38201 Google Scholar[2] Claude Berge, Théorie des graphes et ses applications, Collection Universitaire de Mathématiques, II, Dunod, Paris, 1958viii+277 MR0102822 0088.15404 Google Scholar[3] R. Bott and , J. P. Mayberry, Matrices and trees, Economic activity analysis, John Wiley and Sons, Inc., New York, 1954, 391–400 MR0067067 0057.12402 Google Scholar[4] R. L. Brooks, , C. A. B. Smith, , A. H. Stone and , W. T. Tutte, The dissection of rectangles into squares, Duke Math. J., 7 (1940), 312–340 10.1215/S0012-7094-40-00718-9 MR0003040 0024.16501 CrossrefGoogle Scholar[5] Frank Harary, A graph theoretic method for the complete reduction of a matrix with a view toward finding its eigenvalues, J. Math. Phys., 38 (1959/1960), 104–111 MR0109793 0087.01701 CrossrefGoogle Scholar[6] Frank Harary, A graph theoretic approach to matrix inversion by partitioning, Numer. Math., 4 (1962), 128–135 10.1007/BF01386304 MR0139545 0109.09003 CrossrefGoogle Scholar[7] Frank Harary, The determinant of the adjacency matrix of a graph, SIAM Rev., 4 (1962), 202–210 10.1137/1004057 MR0144330 0113.17406 LinkISIGoogle Scholar[8] Frank Harary, , Robert Z. Norman and , Dorwin Cartwright, Structural models: An introduction to the theory of directed graphs, John Wiley & Sons Inc., New York, 1965ix+415 MR0184874 0139.41503 Google Scholar[9] G. Kirchhoff, Über die Auflösung der Gleichungen, auf welche man bei der Untersuchungen der linearen Verteilung galvanischer Ströme geführt wird, Poggendorf Ann., 72 (1847), 497–508 CrossrefGoogle Scholar[10] W. T. Tutte and , C. A. B. Smith, On Unicursal Paths in a Network of Degree 4, Amer. Math. Monthly, 48 (1941), 233–237 MR1525117 0025.09103 CrossrefGoogle Scholar[11] W. T. Tutte, The dissection of equilateral triangles into equilateral triangles, Proc. Cambridge Philos. Soc., 44 (1948), 463–482 MR0027521 0030.40903 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Exploring Spatial Patterns In Sustainable Integrated Districts: A Methodology For Early-Phase Urban Network Analysis2022 Annual Modeling and Simulation Conference (ANNSIM) | 18 Jul 2022 Cross Ref Pining Control Algorithm for Complex Networks2019 Chinese Control Conference (CCC) | 1 Jul 2019 Cross Ref A GPU-Adapted Structure for Unstructured GridsComputer Graphics Forum, Vol. 36, No. 2 | 23 May 2017 Cross Ref Image smoothing with generalized random walks: Algorithm and applicationsApplied Soft Computing, Vol. 46 | 1 Sep 2016 Cross Ref A Constrained Guess-Check Approach for Resource Allocation in the Robot Control System DesignAdvances in Reconfigurable Mechanisms and Robots II | 24 November 2015 Cross Ref Automatic aid for robot control system design2015 International Conference on Advanced Robotics (ICAR) | 1 Jul 2015 Cross Ref Retaining connectivity in multi-task communications network with multiple agents: Connectability theory approach2013 American Control Conference | 1 Jun 2013 Cross Ref Predictive modeling and retaining connectivity for mobile wireless communication network2012 IEEE Conference on Technologies for Homeland Security (HST) | 1 Nov 2012 Cross Ref Uncooperative multi-agent communication network control, hybrid LQ approach2012 American Control Conference (ACC) | 1 Jun 2012 Cross Ref Preventing disruption of a mobile communication network using Higher Order Sliding Mode control49th IEEE Conference on Decision and Control (CDC) | 1 Dec 2010 Cross Ref The weighted complexity and the determinant functions of graphsLinear Algebra and its Applications, Vol. 433, No. 2 | 1 Aug 2010 Cross Ref Reconfiguration of a mobile communication network via Higher-Order Sliding Mod