Cohen-Macaulayness of two classes of circulant graphs. (English) Zbl 1467.05210
Summary: Let \(n\) be a positive integer and let \(S_n\) be the set of all nonnegative integers less than \(n\) which are relatively prime to \(n\). In this paper, we discuss structural properties of circulant graphs generated by the \(S_n\)’s and their complements. In particular, we characterize when these graphs are well-covered, Cohen-Macaulay, Buchsbaum or Gorenstein.
MSC:
| 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 |
Keywords:
circulant graph; well-covered graph; Cohen-Macaulay graph; Buchsbaum graph; Gorenstein graph; \(f\)-vectorReferences:
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