“…Conjugated-carbon nano-structures have played a central part in chemistry for well over a century, with intense interest (and three Nobel prizes) during the last couple of decades for work on conjugated (possibly metallically conducting) polymers [1,2], novel fullerene cages [3] and single-layer graphene [4,5]. But also comparable experimental interest has developed concerning carbon nanotubes [6,7], graphenic strips [8,9] and different modest decorations to these species, while interest in traditional benzenoids has been maintained, and much extended [10][11][12]; further, for graphene, as well as large benzenoids and buckytubes, much interest has developed regarding decorations [13][14][15][16][17][18]. In the last few decades, 'chemical graph theory' has developed, with a significant fraction of the work directed [19][20][21][22] towards conjugated π -networks in the context of the tight-binding Hückel model, although only a rather modest effort was initially directed [23][24][25][26][27][28] to the HOMO-LUMO gap.…”