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Edge ideals; Betti numbers; regularity.

To every finite simple graph $G$, we associate the so-called edge ideal $I (G)$, which is a square-free quadratic monomial ideal generated by the monomials corresponding to the edges of $G$. In this paper, we determine all the initial graded Betti numbers of edge ideals of triangular graphs and alternate triangular graphs in terms of the underlying graph. We also compute the regularity of edge ideals of triangular and alternate triangular graphs.

SHAHNAWAZ AHMAD RATHER¹ PAVINDER SINGH¹ ROHIT VERMA¹

1. Department of Mathematics, Central University of Jammu, Rahya-Suchani (Bagla), Samba 181 143, India

Published

6 August 2020

Final version published online

6 August 2020