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Altanisation (formation of the altan of a parent structure) originated in thechemical literature as a formal device for constructing generalised coronenesfrom smaller structures. The altan of graph $G$, denoted $\mathfrak{a}(G, H)$,depends on the choice of attachment set $H$ (a cyclic $h$-tuple of vertices of$G$). From a given pair $(G, H)$, the altan construction produces a pair $(G',H')$, where $H'$ is called the induced attachment set. Repetition of theconstruction, using at each stage the attachment set induced in the previousstep, defines the iterated altan. Here, we prove sharp bounds for the nullityof altan and iterated altan graphs based on a general parent graph: for anyattachment set with odd $h$, nullities of altan and parent are equal; for any$h$ and all $k \geq 1$, the $k$-th altan has the same nullity as the first; forany attachment set with even $h$, the nullity of the altan exceeds the nullityof the parent graph by one of the three values $\{0, 1, 2\}$. The case ofexcess nullity $2$ has not been noticed before; for benzenoids with the naturalattachment set consisting of the CH sites, it occurs first for a parentstructure with $5$ hexagons. On the basis of extensive computation, it isconjectured that in fact no altan of a convex benzenoid has excess nullity $2$.

On the Nullity of Altans and Iterated Altans