On Restricted Coloring Problems Of Some Special Graphs

A (d, 1)-total labelling of a graph G is a function f from (V(G), E(G))to the set {0, 1,…k} such that f(ui)≠f(uj) if ui and uj are two adjacentvertices,f(ei)≠(ej) if ei and ei are two adjacent edges, and f (ui)-f(ej)≥d if an edge ej is incident to a vertex ui The span of a (d, 1)-totallabelling is the maximum difference between two labels. The mimimumspan of a (d, 1)-total labelling of G is called the (d, 1)-total number anddenoted by≠Td (G).For the direct product graphs Pm×Cn and Pm×Kn,wecompletely determine their (d, 1)-total number. We also obtain the [r,s,1]-chromatic number of even complete graph, where r≥2 and r+2...