Let G = (V, E) be a finite simple graph with the vertex set V = {x1, . . . , xn}. We identify the vertices of the graph with the variables in the polynomial ring R = k[x1, . . . , xn] where k is a fixed field. The closed neighborhood ideal of G denoted by NI(G), is defined as an ideal in R generated by all monomials of the form Q xj∈N[xi] xj , where xi ∈ V . Here N[xi] is the closed neighborhood of xi in G, which is the set {xi} ∪ {xj ; {xi, xj} ∈ E} In this talk we study some algebraic invariants of these ideals like CastelnuovoMumford regularity and projective dimension and present some combinatorial descriptions for these invariants in terms of graph invariants.
This is a joint work with Somayeh Moradi.

https://zoom.us/join
Meeting ID: 908 611 6889
Passcode: 362880