A new construction for Cohen-Macaulay graphs

الأصل · EN

Let G be a finite simple graph on a vertex set V(G)={x₁₁,, xₙ₁}. Also let m₁,,mₙ ≥ 2 be integers and G₁,, Gₙ be connected simple graphs on the vertex sets V(Gᵢ)={xᵢ₁,, ximᵢ}. In this paper, we provide necessary and sufficient conditions on G₁,, Gₙ for which the graph obtained by attaching Gᵢ to G is unmixed or vertex decomposable. Then we characterize Cohen--Macaulay and sequentially Cohen--Macaulay graphs obtained by attaching the cycle graphs or connected chordal graphs to an arbitrary graphs.