Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An L(2,1)-labeling of a graph is a mapping c:V(G)→\0,\ldots,K\ such that the labels assigned to neighboring vertices differ by at least 2 and the labels of vertices at distance two are different. Griggs and Yeh [SIAM J. Discrete Math. 5 (1992), 586―595] conjectured that every graph G with maximum degree Δ has an L(2,1)-labeling with K≤Δ ^2.  verify the conjecture for planar graphs with maximum degree Δ ≠3.
['Peter Bella', 'Daniel Král', 'Bojan Mohar', 'Katarína Quittnerová']
I am writing a research paper on a idea Labeling planar graphs with a condition at distance two
[{"from": "human", "value": "I am writing a research paper on a idea Labeling planar graphs with a condition at distance two"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An L(2,1)-labeling of a graph is a mapping c:V(G)\u2192\\0,\\ldots,K\\ such that the labels assigned to neighboring vertices differ by at least 2 and the labels of vertices at distance two are different. Griggs and Yeh [SIAM J. Discrete Math. 5 (1992), 586\u2015595] conjectured that every graph G with maximum degree \u0394 has an L(2,1)-labeling with K\u2264\u0394 ^2.  verify the conjecture for planar graphs with maximum degree \u0394 \u22603."}]