Abstract
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.
Highlights
Introduction and preliminariesMetal organic framework (MOF) is a graph that consists of metal atoms
These atoms are linked with the help of organic ligands which acts like a linker, having large pore volume which is known as pours coordination polymer
That is represented by a graph G, metal atoms and organic ligands are represented by vertices and edges, respectively (Hasan and Jhung, 2015; Jiao et al, 2019; Liu et al, 2014; Pettinari et al, 2017)
Summary
Metal organic framework (MOF) is a graph that consists of metal atoms These atoms are linked with the help of organic ligands which acts like a linker, having large pore volume which is known as pours coordination polymer. The fractional metric dimesnison of G is denoted by and defined as where Metric dimension has several applications in chemistry, e.g., the substructures of a chemical compound which can be denoted by a set of functional groups. For 1 ≤ k ≤ n, j = i + 1, i Î [2k − 1], and 1 ≤ t ≤ n: Proof: The resolving neighborhoods of metal organic framework for is: with, Lemma 2 Let MOF (n) be the metal organic frame work for n ≥ 8 (n≡ 0(mod).,for (a) and (l).
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