Mixed metric dimension of graphs with edge disjoint cycles

In a connected graph G , the cardinality of smallest ordered set vertices that distinguishes every element V ( ) ? E is called mixed metric dimension . this paper we first establish exact value unicyclic which derived from structure We further consider graphs with edge disjoint cycles, where for each cycle C i define subgraph in only cycle. Applying result to then yields such The obtained formulas yield simple sharp upper bound on dimension, and conclude conjecturing analogous holds general prescribed cyclomatic number.