  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 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.
