On potentially Kr1,r2,....rm-graphic sequencesi

For given a graph II, a graphic sequence pi = (d(1), d(2), . . . , d(n)) is said to be potentially H-graphic if there exists a realization of pi containing H as a subgraph. In this paper, we determine the smallest even integer sigma(K-1s,t,n) such that each n-term graphic sequence with term sum at least sigma(K-1s,t,n) is potentially K-1s,t-graphic, where n >= 3s+2t(2) +3t-3 and K-1(s),t is an r(1) x r(1) x (. . .) x r(s+1) complete s + 1-partite graph with r(1) = r(2) = (. . .) = r(s) = 1 and r(s+1) = t. Moreover, we also characterize the potentially K-r,K-s-graphic sequences without zero terms for r = 2, s = 3 and r = 2, s = 4, where K-r,K-s is an r x s complete bipartite graph.