Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The edge-bandwidth of a graph G is the smallest number B' for which there is a bijective labeling of E(G) with {1,...,e(G)} such that the difference beten the labels at any adjacent edges is at most B'. Here  compute the edge-bandwidth for rectangular grids: B'(Pm⊕Pn)=2 min(m,n) - 1 if max(m,n) ≥ 3, where ⊕ is the Cartesian product and Pn denotes the path on n vertices. This settles a conjecture of Calamoneri et al. [New results on edge-bandwidth, Theoret. Comput. Sci. 307 (2003) 503-513].  also compute the edge-bandwidth of any torus (a product of two cycles) within an additive error of 5.
['Oleg Pikhurko', 'Jerzy Wojciechowski']
I am writing a research paper on a idea Edge-bandwidth of grids and tori
[{"from": "human", "value": "I am writing a research paper on a idea Edge-bandwidth of grids and tori"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The edge-bandwidth of a graph G is the smallest number B' for which there is a bijective labeling of E(G) with {1,...,e(G)} such that the difference beten the labels at any adjacent edges is at most B'. Here  compute the edge-bandwidth for rectangular grids: B'(Pm\u2295Pn)=2 min(m,n) - 1 if max(m,n) \u2265 3, where \u2295 is the Cartesian product and Pn denotes the path on n vertices. This settles a conjecture of Calamoneri et al. [New results on edge-bandwidth, Theoret. Comput. Sci. 307 (2003) 503-513].  also compute the edge-bandwidth of any torus (a product of two cycles) within an additive error of 5."}]