Turkish Journal of Mathematics
Abstract
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.
DOI
10.3906/mat-1801-71
Keywords
Chordal graph, zero-divisor graph, total graph, Jacobson graph, unit graph, comaximal graph, dot product graphs
First Page
2202
Last Page
2213
Recommended Citation
NIKSERESHT, ASHKAN
(2018)
"Chordality of graphs associated to commutative rings,"
Turkish Journal of Mathematics: Vol. 42:
No.
5, Article 10.
https://doi.org/10.3906/mat-1801-71
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss5/10
