Two-Step Colouring of Grid Graphs of Different Types

In this article, we consider the NP-hard problem of two-step colouring a graph. It is required to colour graph in given number colours way, when no pair vertices has same colour, if these are at distance 1 or 2 between each other. The optimum one that uses minimum possible colours.The studied application grid graphs. We four types grids: triangular, square, hexagonal, and octogonal. show hexagonal octogonal graphs requires 4 general case. formulate polynomial algorithms for such colouring. A square with maximum vertex degree equal 3 5 paper, suggest backtracking algorithm Also, present algorithm, which works linear time relative vertices, 7 triangular always correct. If equals 6, solution optimum.