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.
Graphs with loops, linear quotients, ideals of vertex covers, Cohen-Macaulay ideals
IMBESI, MAURIZIO and BARBIERA, MONICA LA
"Vertex covers in graphs with loops,"
Turkish Journal of Mathematics: Vol. 42:
3, Article 35.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/35