| Abstrakt: |
Let H = { H v : v ∈ V (G) } be a family of nonempty graphs indexed by the vertex set of a graph G. The corona G ∘ H of G and H is the disjoint union of G and H v , v ∈ V (G) , with additional edges joining each vertex v ∈ V (G) to all the vertices of H v . In this paper, we show that the corona graph G ∘ H is Cohen–Macaulay if and only if G ∘ H is a clique corona graph, i.e., all graphs H v in H are complete graphs. In addition, if I denotes the edge ideal of the clique corona graph G ∘ H , we prove that the Castelnuovo–Mumford regularity of R/I is equal to the induced matching number of G ∘ H . [ABSTRACT FROM AUTHOR] |
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