On determining number and metric dimension of zero-divisor graphs
Abstract
In this article, explicit formulas for finding the determining number and the metric dimension of the zero-divisor graph of Zn and non-Boolean semisimple rings are given. In the case of Boolean rings, an upper bound of the determining number and the metric dimension of zero-divisor graph is determined. Further, the determining number and the metric dimension of some important graphs other than zero-divisor graphs, are proved and the open problem by Boutin, regarding the determining number of graphs is settled.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.