Computation of edge resolvability of benzenoid tripod structure (Q2051719)

Summary: In chemistry, graphs are commonly used to show the structure of chemical compounds, with nodes and edges representing the atom and bond types, respectively. Edge resolving set \(\lambda_e\) is an ordered subset of nodes of a graph \(C\), in which each edge of \(C\) is distinctively determined by its distance vector to the nodes in \(\lambda\). The cardinality of a minimum edge resolving set is called the edge metric dimension of \(C\). An edge resolving set \(L_{e, f}\) of \(C\) is fault-tolerant if \(\lambda_{e, f}\setminus b\) is also an edge resolving set, for every \(b\) in \(\lambda_{e, f}\). Resolving set allows obtaining a unique representation for chemical structures. In particular, they were used in pharmaceutical research for discovering patterns common to a variety of drugs. In this paper, we determine the exact edge metric and fault-tolerant edge metric dimension of benzenoid tripod structure and proved that both parameters are constant.