Abstract :
A graph G of order n and size m is edge-magic if there is a bijection image such that all sums image, image, are the same. We present new lower and upper bounds on image, the maximum size of an edge-magic graph of order n, being the first to show an upper bound of the form image. Concrete estimates for image can be obtained by knowing image, the maximum number of distinct pairwise sums that a k-subset of image can have.s(k,n)⩽n+k214-1(π+2)2+o(1)
Keywords :
Additive basis , Edge-magic graph , Sidon set , Quasi-Sidon set , Sum-set
