Edge-counting vectors, Fibonacci cubes, and Fibonacci triangle

Edge-counting vectors of subgraphs of Cartesian products are intro- duced as the counting vectors of the edges that project onto the factors. For several standard constructions their edge-counting vectors are computed. It is proved that the edge-counting vectors of Fibonacci cubes are precisely the rows of the Fibonacci trian- gle and that the edge-counting vectors of Lucas cubes are Fn 1-constant vectors. Some problems are listed along the way.

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