Título:
|
Optimal grid drawings of complete multipartite graphs and an integer variant of the algebraic connectivity
|
Autor/a:
|
Fabila Monroy, Ruy; Hidalgo Toscano, Carlos; Huemer, Clemens; Lara, Dolores; Mitsche, Dieter
|
Otros autores:
|
Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. DCG - Discrete and Combinatorial Geometry |
Abstract:
|
How to draw the vertices of a complete multipartite graph G on different points of a bounded d-dimensional integer grid, such that the sum of squared distances between vertices of G is (i) minimized or (ii) maximized? For both problems we provide a characterization of the solutions. For the particular case d = 1, our solution for (i) also settles the minimum-2-sum problem for complete bipartite graphs; the minimum2-sum problem was defined by Juvan and Mohar in 1992. Weighted centroidal Voronoi tessellations are the solution for (ii). Such drawings are related with Laplacian eigenvalues of graphs. This motivates us to study which properties of the algebraic connectivity of graphs carry over to the restricted setting of drawings of graphs with integer coordinates. |
Materia(s):
|
-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs -Graph theory -multipartite graph -algebraic connectivity -Voronoi diagram -grid drawing -Grafs, Teoria de |
Derechos:
|
|
Tipo de documento:
|
Artículo - Versión presentada Objeto de conferencia |
Editor:
|
Springer
|
Compartir:
|
|