Exploring the fault-tolerant metric dimension (FTMD) of the M-polynomial for zigzag edge coronoids fused with starphene

Abstract

Graph invariants are valuable tools for exploring the complex structures of molecular graphs, which have attracted significant interest from researchers across multiple disciplines. Graph theory plays a crucial role in understanding chemical structures and their real-world applications. By representing chemical compounds as graphs, we can dive deeper into their theoretical properties and uncover meaningful insights. One important measure in graph theory is the metric dimension, which tells us the minimum number of vertices needed to uniquely identify all others within a graph. The fault-tolerant metric dimension (FTMD) takes this a step further, ensuring that even if some vertices or edges fail, identification remains intact. In this research, we apply both FTMD and partition dimension to molecular graphs, focusing specifically on the unique structure of the \M-polynomial of zigzag edge coronoid fused with starphene. Through graph theory, we gain a better understanding of this molecule's intricate architecture.