We investigate when different graphs associated to commutative rings are chordal. In particular, we characterize commutative rings $R$ with each of the following conditions: the total graph of $R$ is chordal; the total dot product or the zero-divisor dot product graph of $R$ is chordal; the comaximal graph of $R$ is chordal; $R$ is semilocal; and the unit graph or the Jacobson graph of $R$ is chordal. Moreover, we state an equivalent condition for the chordality of the zero-divisor graph of an indecomposable ring and classify decomposable rings that have a chordal zero-divisor graph.
Chordal graph, zero-divisor graph, total graph, Jacobson graph, unit graph, comaximal graph, dot product graphs
"Chordality of graphs associated to commutative rings,"
Turkish Journal of Mathematics: Vol. 42:
5, Article 10.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss5/10