Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Some graphs admit drawings in the Euclidean k-space in such a (natural) way, that edges are represented as line segments of unit length. Such embeddings are called k-dimensional unit distance representations. The embedding is strict if the distances of points representing nonadjacent pairs of vertices are different than 1.When two nonadjacent vertices are drawn in the same point,  say that the representation is degenerate. Computational complexity of nondegenerate embeddings has been studied before.  initiate the study of the computational complexity of (possibly) degenerate embeddings. In particular  prove that for every k≥ 2, deciding if an input graph has a (possibly) degenerate k-dimensional unit distance representation is NP-hard.
['Boris Horvat', 'Jan Kratochvíl', 'Tomaž Pisanski']
I am writing a research paper on a idea On the computational complexity of degenerate unit distance representations of graphs
[{"from": "human", "value": "I am writing a research paper on a idea On the computational complexity of degenerate unit distance representations of graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Some graphs admit drawings in the Euclidean k-space in such a (natural) way, that edges are represented as line segments of unit length. Such embeddings are called k-dimensional unit distance representations. The embedding is strict if the distances of points representing nonadjacent pairs of vertices are different than 1.When two nonadjacent vertices are drawn in the same point,  say that the representation is degenerate. Computational complexity of nondegenerate embeddings has been studied before.  initiate the study of the computational complexity of (possibly) degenerate embeddings. In particular  prove that for every k\u2265 2, deciding if an input graph has a (possibly) degenerate k-dimensional unit distance representation is NP-hard."}]