Does Topology-Dependent Chemistry Influence the Interstellar PAH Inventory? Insights from the Absence of Cyanotriphenylenes

Although a set of polycyclic aromatic hydrocarbons (PAHs) has recently been identified in the cold dark cloud TMC-1, several common PAH motifs remain absent, leaving the origin of this apparent structural selectivity unresolved. Triphenylene (\ce{C18H12}) provides a stringent test of whether relative thermodynamic stability alone can account for the emerging PAH inventory because it is the smallest fully benzenoid PAH predicted by Clar's rule, is exceptionally stable, and is a key subunit of larger detected aromatic frameworks such as coronene and fullerene-related species. To probe whether such thermodynamically favored carbon skeletons are selected under cold interstellar conditions, we synthesized cyanotriphenylenes and measured their first 6.5--16~GHz microwave rotational spectra as polar tracers for the non-polar parent. An astronomical search based on these spectroscopic parameters yielded no detection, suggesting a possible ``missing triphenylene'' anomaly: despite its exceptional thermodynamic stability, this fully benzenoid PAH may be relatively depleted in TMC-1. To rationalize this behavior, we introduce a ring-node graphic representation that classifies PAH skeletons by topology; within this framework, triphenylene, whose compactness is otherwise ambiguous, is classified as non-compact. This representation reveals a tentative clustering of the currently detected and undetected PAHs according to topology, suggesting that the current PAH inventory cannot be rationalized solely on the basis of thermodynamic stability and may instead reflect differences in formation and destruction kinetics. The observed selectivity may arise from two complementary effects: sequential growth decay along bottom-up growth pathways and rapid consumption of bay-region intermediates by reactive unsaturated small species.