17 research outputs found
Optimal Grid Drawings of Complete Multipartite Graphs and an Integer Variant of the Algebraic Connectivity
How to draw the vertices of a complete multipartite graph on different
points of a bounded -dimensional integer grid, such that the sum of squared
distances between vertices of is (i) minimized or (ii) maximized? For both
problems we provide a characterization of the solutions. For the particular
case , our solution for (i) also settles the minimum-2-sum problem for
complete bipartite graphs; the minimum-2-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.Comment: Appears in the Proceedings of the 26th International Symposium on
Graph Drawing and Network Visualization (GD 2018
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum