Fault-Tolerant Metric Dimension (FTMD) of M-polynomial of Zigzag Edge Coronoid Fused by Starphene

Abstract

The application of graph invariants serves as a valuable tool for analyzing the complex structures of molecular graphs, attracting researchers across various fields. Graph theory has played a pivotal role in explaining chemical structures and finding practical applications. Representing chemical compounds as graphs enable theoretical exploration and yield meaningful insights. Among graph parameters, metric dimension stands out as a key metric, quantifying the minimum vertices needed for unique identification within a graph. The concept of fault-tolerant metric dimensions extends this idea, considering identification robustness in the face of faulty vertices or edges. This research applies metric dimension and fault-tolerant metric dimension to molecular graphs and networks, with a focus on the unique structural properties of the "M-polynomial of zigzag edge coronoid fused by starphene" molecule. Through graph theory, we deepen our understanding of this compound's intricate molecular architecture. Mathematics Subject Classification 2023: 05C12