A simple graph-theory-based model is put forward, by means of which it is possible to express the energy difference between geometrically non-equivalent forms of a conjugated polyene. This is achieved by modifying the adjacency matrix of the molecular graph, and including into it information on cis/trans constellations. The total π-electron energy thus calculated is in excellent agreement with the enthalpies of the underlying isomers and conformers. [Projekat Ministarstva nauke Republike Srbije, br. 174033]