Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24491220200901The regularity of binomial edge ideals of graphs217221392910.22060/ajmc.2020.16433.1024ENSaraSaeedi MadaniFaculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic),Tehran, IranDariushKianiFaculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic),Tehran, IranJournal Article20190528In 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.https://ajmc.aut.ac.ir/article_3929_b83d4acf2f2cd01f5b330abd203696c6.pdf