@techreport{TR-IC-05-13, number = {IC-05-13}, author = {C. N. Campos and C. P. de Mello}, title = {The total chromatic number of some bipartite graphs}, month = {June}, year = {2005}, institution = {Institute of Computing, University of Campinas}, note = {In English, 11 pages. \par\selectlanguage{english}\textbf{Abstract} The total chromatic number $nct(G)$ is the least number of colours needed to colour the vertices and edges of a graph $G$ such that no incident or adjacent elements (vertices or edges) receive the same colour. This work determines the total chromatic number of grids, particular cases of partial grids, near-ladders, and of $k$-dimensional cubes. } }