Luis A. Dupont-García, Emanuel Portilla-Cruz, Armando Sánchez-Nungaray: The zero-divisor graph of the edge-ring of a simple graph, 43-60

Abstract:

We study the zero-divisor graph for a commutative ring R denoted by $\Gamma(R)$, this for the ring of edges $R(\mathcal{G})$ of a simple graph $\mathcal{G}$. Based on the graph $\Gamma(R(\mathcal{G}))$, we characterize the ring of edges with the graph invariants diameter and girth. Moreover, for this family of graphs, we compute the clique number and the chromatic number, obtaining that this family of graphs is weakly perfect.

Key Words: Monomial ideal, edge ideal, Stanley decompositions, Stanley depth.

2020 Mathematics Subject Classification: Primary 05E40; Secondary 05C25, 13F55, 13A70.

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