Metric Dimension of Signed Unit Graphs

Resumo

This paper determines the metric dimension of the signed unit graph $G_{\Sigma}(R)$ associated with a finite commutative ring $R$. Explicit formulas and bounds have been established for the metric dimension of signed unit graph for several classes of rings. Further, we have characterized the rings for which the metric dimension of the signed unit graph is equal to metric dimension of its underlying graph.