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Vertex covers in graphs with loops. (English) Zbl 1424.05138

Summary: We investigate ideals of vertex covers for the edge ideals associated to considerable classes of connected graphs with loops and exhibit algebraic information about them, such as the existence of linear quotients, the computation of invariant values, and the Cohen-Macaulay property. These algebraic procedures are good instruments for evaluating situations of minimal node coverings in networks.

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
13C14 Cohen-Macaulay modules
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