We provide some exact formulas for the projective dimension and regularity of edge ideals
associated to some vertex-weighted oriented cyclic graphs with a common vertex or edge …

In this paper we provide some exact formulas for the projective dimension and the regularity
of edge ideals of vertex-weighted oriented unicyclic graphs. These formulas are in function …

In this paper we will provide the exact formulas for the regularity and projective dimension of
edge ideals of three types of vertex-weighted oriented m-partite graphs. We also give some …

We provide formulas for the projective dimension and the regularity of edge ideals
associated to vertex weighted rooted forests and oriented cycles. We derive from that exact …

Let t be any positive integer and I (C n) the edge ideal of a vertex-weighted oriented n-cycle
graph C n. We provide explicit formulas for the regularity and depth of I (C n) t. In particular …

In this paper we provide some exact formulas for the regularity of powers of edge ideals of
vertex-weighted oriented cycles and vertex-weighted unicyclic graphs. These formulas are …

In this paper we provide some exact formulas for the projective dimension and the regularity
of edge ideals associated to three special types of vertex-weighted oriented $ m $-partite …

For any finite simple graph G one can associate a simplicial complex Δ (G) and an edge
ideal I (G). We attempt to use the combinatorial properties of the given graph to understand …

In this paper, we compute the projective dimension of the edge ideals of graphs consisting of
some cycles and lines which are joint in a common vertex. Moreover, we show that for such …

ARITHMETICAL RANK OF THE CYCLIC AND BICYCLIC GRAPHS Page 1 Journal of
Algebra and Its Applications Vol. 11, No. 2 (2012) 1250039 (14 pages) c© World Scientific …