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Mixed Metric Dimension of Cartesian Product of Graph

Last modified: 2021-11-19

#### Abstract

A set of vertices *S* *mixed-resolves* a graph *G* if every vertices or edges is uniquely determined by its vector of distances to the vertices in *S*. The *mixed metric dimension* of *G* is the minimum cardinality of a mixed resolving set of *G*. This paper studies some upper bounds for the mixed metric dimensions of the Cartesian product for any given graph *G* and *H* and the exact value of the mixed metric dimension of the Cartesian product for a particular graph *G* and *H*.