Computing Bounds of Fractional Metric Dimension of Metal Organic Graphs
Mohsin Raza, Dalal Awadh Alrowaili, Muhammad Javaid, Khurram Shabbir · Journal of Chemistry · 2021
Metal organic graphs are hollow structures of metal atoms that are connected by ligands, where metal atoms are represented by the vertices and ligands are referred as edges. A vertex x resolves the vertices u and v of a graph G if d u , x ≠ d v , x . For a pair u , v of vertices of G , R u , v = x ∈ V G : d x , u ≠ d x , v is called its resolving neighbourhood set. For each pair of vertices u and v in V G , if f R u , v ≥ 1 , then f from V G to the interval 0,1 is called resolving function. Moreover, for two functions f and g , f is called minimal if f ≤ g and f v ≠ g v for at least one v ∈ V G . The fractional metric dimension (FMD) of G is denoted by dim