In this paper, we present some lower bounds and upper bounds on the arithmetical rank of the edge ideals of some n-cyclic graphs with a common edge. For some special n-cyclic graphs with a common edge, we prove that the arithmetical rank equals the projective dimension of the corresponding quotient ring.
Arithmetical rank, edge ideal, projective dimension, set-theoretic complete intersection
ZHU, GUANGJUN; SHI, FENG; and GU, YAN
"Arithmetical rank of the edge ideals of some n-cyclic graphs with a common edge,"
Turkish Journal of Mathematics: Vol. 39:
1, Article 11.
Available at: https://journals.tubitak.gov.tr/math/vol39/iss1/11