HOMOLOGICAL INVARIANTS OF CAMERON-WALKER GRAPHS

Let G be a finite simple connected graph on [n] and R = K[x(1), ..., x(n)] the polynomial ring in n variables over a field K. The edge ideal of G is the ideal I(G) of R which is generated by those monomials x(i)x(j) for which {i, j} is an edge of G. In the present paper, the possible tuples (n, depth(R/I(G)), reg(R/I(G)), dim R/I(G), deg h(R/I(G))), where deg h(R/I(G)) is the degree of the h-polynomial of R/I(G), arising from Cameron-Walker graphs on [n] will be completely determined.