Apologies I am a layman with regards to graph theory and am curious about the problem here as it might relate to materials science (hence $2$ or $3$ dimensions). References and paper recommendations are welcomed.
Given a finite set of degrees, where the number of elements corresponds to the number vertices/unit cell, is provided, is there a specific algorithm to generate a corresponding periodic geometric graph in which no two edges intersect? An example is shown below where the left represents a valid periodic planar (2D) graph composed of the set of degrees {$1, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5$}.
