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

Abstract

Lee and Kong conjecture that if \(n \geq 1\) is an odd number, then \(St(a_1, a_0, \ldots, a_n)\) would be super edge-magic, and meanwhile they proved that the following graphs are super edge-magic: \(St(m,n)\) (\(n = 0 \mod (m+1)\)), \(St(1,k,n)\) (\(k = 1,2\) or \(n\)), \(St(2, k,n)\) (\(k = 2,3\)), \(St(1,1,k,n)\) (\(k = 2,3\)), \(St(k,2,2,n)\) (\(k = 1,2\)). In this paper, the conjecture is further discussed and it is proved that \(St(1,m,n)\), \(St(3,m,m+1)\), \(St(n,n+1,n+2)\) are super edge-magic, and under some conditions \(St(a_1, a_2, \ldots, a_{2n+1})\); \(St(a_1, a_2, \ldots, a_{4n+1})\), \(St(a_1, a_2, \ldots, a_{4n+3})\) are also super edge-magic.