Sohail ZafarSchenzel, Peter2014-04-302014-04-302014Schenzel, P., & Zafar, S. (2014). Algebraic properties of the binomial edge ideal of a complete bipartite graph, to appear in An. St. Univ. Ovidius Constanta, Ser. Mat, 22(2), 217-237.https://escholar.umt.edu.pk/handle/123456789/1124Let JG denote the binomial edge ideal of a connected undirected graph on n vertices. This is the ideal generated by the binomials xiyj 􀀀 xjyi; 1 i < j n; in the polynomial ring S = K[x1; : : : ; xn; y1; : : : ; yn] where fi; jg is an edge of G. We study the arithmetic properties of S=JG for G, the complete bipartite graph. In particular we compute dimen- sions, depths, Castelnuovo-Mumford regularities, Hilbert functions and multiplicities of them. As main results we give an explicit description of the modules of de ciencies, the duals of local cohomology modules, and prove the purity of the minimal free resolution of S=JG.enArticle