Some results on the multipartite Ramsey numbers m(j)(C(3),C(m),n(1)K(2),n(2)K(2),…,n(i)K(2))

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