Document Type : Original Article
Mathematics department, Mathematics and Computer Science faculty, Amirkabir University of Technology, Tehran, Iran
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
In this paper, we study the Castelnuovo-Mumford regularity and the graded Betti numbers of the binomial edge ideals of some classes of graphs. Our special attention is devoted to a conjecture which asserts that the number of maximal cliques of a graph provides an upper bound for the regularity of its binomial edge ideal.