Some Discussions on Super Edge-Magic Labelings of St(a_1,...,a_n)

摘要

Lee and Kong conjecture that if n ≥ 1 is an odd number, then St(a_1, a_2,...,a_n) would be super edge-magic, and meanwhile they proved that the following graphs are super edge-magic: St(m, n) (n ≡Omod(m+1)), St(l, k, n) (k = l,2 or n), St(2, k, n) (k = 2, 3), St(1,l, k, n)(k = 2, 3), St(k,2, 2, n) (k = 1, 2). In this paper, the conjecture is further discussed and it is proved that St(l, m, n), St(3, m, m+1), St(n, n +1, n+2) are super edge-magic, and under some conditions St(a_1, a_2,...,a_(2n+1),St(a_1, a_2,...,a_(4n+1)), St(a_1, a_2,...,a_(4n+3)) are also super edge-magic.