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Let $\Gamma=(V,E)$ be a simple connected graph.$d(\alpha,\epsilon)=min\{d(\alpha, w), d(\alpha, d\}$ computes the distancebetween a vertex $\alpha \in V(\Gamma)$ and an edge $\epsilon=wd\in E(\Gamma)$.A single vertex $\alpha$ is said to recognize (resolve) two different edges$\epsilon_{1}$ and $\epsilon_{2}$ from $E(\Gamma)$ if $d(\alpha,\epsilon_{2})\neq d(\alpha, \epsilon_{1}\}$. A subset of distinct orderedvertices $U_{E}\subseteq V(\Gamma)$ is said to be an edge metric generator for$\Gamma$ if every pair of distinct edges from $\Gamma$ are recognized by someelement of $U_{E}$. An edge metric generator with a minimum number of elementsin it, is called an edge metric basis for $\Gamma$. Then, the cardinality ofthis edge metric basis of $\Gamma$, is called the edge metric dimension of$\Gamma$, denoted by $edim(\Gamma)$. The concept of studying chemicalstructures using graph theory terminologies is both appealing and practical. Itenables chemical researchers to more precisely and easily examine variouschemical topologies and networks. In this article, we investigate a fascinatingcluster of organic chemistry as a result of this motivation. We consider azigzag edge coronoid fused with starphene and find its minimum vertex and edgemetric generators.

Metric and Edge Metric Dimension of Zigzag Edge Coronoid Fused with Starphene