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, A (2018). Chordality of graphs associated to commutative rings. Turkish Journal of Mathematics 42 (5): 2202-2213. https://doi.org/10.3906/mat-1801-71
