Topological implications of Y-conjugation for electronic transitions of cyanine dyes

To understand connections between electronic transitions of dyes having related conjugated systems, topological arguments from graph theory are often helpful. Using the Chebyshev expansion of the characteristic polynomials of cyanines, it is shown that the two possible structures of tribranched cyanines, i.e., a strongly out-of-plane orientation of one of the conjugated branches or a Y-conjugation of the entire unsaturated system, are both consistent with the similarities between visible absorption of these compounds and of simple chains. To choose between these two structures, evidence from other sources should be added.