Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

THE RIGIDITY OF RECTANGULAR FRAMEWORKS AND THE LAPLACIAN MATRICES

  • KEUNBAE CHOI (Department of Mathematics, Teachers College, Jeju National University) ;
  • HOSOO LEE (Department of Mathematics, Teachers College, Jeju National University)
  • Received : 2023.05.08
  • Accepted : 2023.06.26
  • Published : 2023.07.30
Download PDF
⟨ Previous Next ⟩

Abstract

In general, the rigidity problem of braced rectangular frameworks is determined by the connectivity of the bipartite graph induced by given rectangular framework. In this paper, we study how to solve the rigidity problem of the braced rectangular framework using the Laplacian matrix of the matrix induced by a braced rectangular framework.

Keywords

Acknowledgement

This research was supported by the 2022 scientific promotion program funded by Jeju National University.

References

  1. E.D. Bolker, and Henry Crapo., Bracing Rectangular Frameworks I, SIAM J. Appl. Math. 36 (1997), 473-490.  https://doi.org/10.1137/0136036
  2. K. Choi, The rigidity of rectangular frameworks, Advanced Studies in Contemporary Mathematics 29 (2020), 99-108. 
  3. J.E. Graver, Counting on frameworks: Mathematics to Aid the design of Rigid Structures, The Mathematical Association of America, United States of America, 2001. 
  4. J. Lee, Y.S. Kwon, and K. Choi, A Study on the Bracing Rectangular Frameworks, J. Korea Soc. Math. Ed. Ser. E: Communications of Mathematical Education 30 (2016), 251-262. 
  5. S.T. Laine, The Grid Bracing Problem and a Generalization, Master's Thesis of Worcester Polytechnic Institute, United States of America, 2006. 
  6. Servatius, Brigitte., Graphs, Digraphs, and the Rigidity of Grids, The UMAP Journal 16 (1995), 37-63. 
  7. R.J. Wilson, and J.J. Wakins, Graphs; An introductory Approach, John Wiley and Sons, Inc. 1990.