Fractional metric dimension of metal-organic frameworks

Abstract Metal-organic frameworks (MOF(n)) are organic-inorganic hybrid crystalline porous materials that consist of a regular array of positively charged metal ions surrounded by organic ‘linker’ molecules. The metal ions form nodes that bind the arms of the linkers together to form a repeating, cage-like structure. Moreover, in a chemical structure or molecular graph, edges and vertices are known as bonds and atoms, respectively. Metric dimension being a subsets of atoms with minimum cardinality is used in the substrcturing of the chemical compounds in the molecular structures. Fractional metric dimension is weighted version of metric dimension that associate a numeric value to the identified subset of atoms. In this paper, we have computed the fractional metric dimension of metal organic framework (MOF(n)) for n ≡ 0(mod)2.