Some results on the multipartite Ramsey numbers ( , , , ,…, ).

The graph is a graph which is complete and multipartite which includes partite sets and vertices in each partite set. The multipartite Ramsey number (M-R-number) is the smallest integer for the mentioned graphs , in a way which for each -edge-coloring of the edges of , contains a monochromatic copy of for at least one . The size of M-R-number for , , the M-R-number for , , the M-R-number for each , , the M-R-number for , and , and the size of M-R-number for and have been calculated in various articles hitherto. We acquire some bounds of M-R-number in this essay in which , and , also the size of M-R-number for each is computed in this paper.