Zigzag hexagonal chains (fibonaccenes) form a classical benzenoid family whose resonance graphs are Fibonacci cubes. Motivated by a question of Nemeth [16], we study instead the \emph{matching toggle graph} \( \mathcal{M}(Z) \) of a zigzag hexagonal chain \( Z \) with \( n \) hexagons, whose vertices are all matchings of \( Z \) and whose edges correspond to adding or deleting a single bond. We prove that \[ \operatorname{md}(\mathcal{M}(Z))=\left\lceil\frac{5n+1}{2}\right\rceil, \] thereby confirming N{\'e}meth's conjectured lattice dimension for zigzag hexagonal chains.
More generally, for a connected graph \( G \) with \( m=|E(G)|\ge 2 \), we show that the degree lower bound \( \operatorname{md}(\mathcal{M}(G))\ge \lceil m/2\rceil \) is attained whenever either \( m \) is even, or \( m \) is odd and \( G \) contains a non-bridge edge. The proof combines the standard identification \( \mathcal{M}(G)\cong \mathcal{I}(L(G)) \) with a lattice embedding scheme based on adjacent-edge pairings. An optimal pairing is certified via a perfect matching in a suitable claw-free line graph, guaranteed by the Sumner-Las Vergnas theorem. Thus the chemical case of fibonaccenes appears as a natural and sharp application of a more general graph-theoretic mechanism.