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Edge ideals and connection problems. (English) Zbl 1329.13050

Summary: Ideals arising from graphs are investigated via Gröbner bases theory in order to introduce algebraic objects useful for applications related to the field of security. In particular, the notion of \(s\)-sequence for the generators of the edge ideal \(I(G)\) of any graph \(G\) is considered, so that a description of the Gröbner basis for the relation ideal \(J\) of the symmetric algebra of \(I(G)\) can be obtained. Based on this approach, the initial ideal of \(J\) with respect to a monomial order is well-determined and defines the edge ideal of a supporting graph \(F\), essential in transmitting.

MSC:

13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
05C99 Graph theory
15A78 Other algebras built from modules
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