Betti numbers of edge ideals of Grimaldi graphs and their complements. (English) Zbl 07896533
Summary: Let \(n \geq 2\) be an integer. The Grimaldi graph \(G(n)\) is defined by taking the elements of the set \(\{0, \dots, n-1\}\) as vertices. Two distinct vertices \(x\) and \(y\) are adjacent in \(G(n)\) if and only if \(\gcd (x+y, n) = 1\). In this paper, we examine the Betti numbers of the edge ideals of these graphs and their complements.
MSC:
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
| 05C75 | Structural characterization of families of graphs |
| 13H10 | Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) |
| 05E40 | Combinatorial aspects of commutative algebra |
| 05E45 | Combinatorial aspects of simplicial complexes |
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