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

Abstract

Lee and Kong conjecture that if $n\ge 1$ is an odd number, then $St(a_1,a_0,\dots ,a_n)$ would be super edge-magic, and meanwhile they proved that the following graphs are super edge-magic: $St(m,n)$ ($n=0\mathrm{mod}(m+1)$), $St(1,k,n)$ ($k=1,2$ 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 $St(a_1,a_2,\dots ,a_{2n+1})$; $St(a_1,a_2,\dots ,a_{4n+1})$, $St(a_1,a_2,\dots ,a_{4n+3})$ are also super edge-magic.