Arithmetical rank of the edge ideals of some n-cyclic graphs with a common edge
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.
Anahtar Kelimeler:
Arithmetical rank, edge ideal, projective dimension, set-theoretic complete intersection
Arithmetical rank of the edge ideals of some n-cyclic graphs with a common edge
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.
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- Corollary 3.17 Let G be an n -cyclic graph consisting of the union of n cycles C and C3t1+2, . . . , 3tk3 with a common edge x , where k1+ k3= n . Then bight (I(G)) = pdR(R/I(G)) = ara (I(G)).
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
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