Some Results on Super Edge Magic \(n\)-Stars

Abstract

For integer \(n \geq 2\), let \(a_1, a_2, a_3, \ldots, a_n\) be an increasing sequence of nonnegative integers, and define the \(n\)-star \(St(a_1, a_2, \ldots, a_n)\) as the disjoint union of the \(n\) star graphs \(K(1, a_1), K(1, a_2), \ldots, K(1, a_n)\). In this paper, we have partially settled the conjecture by Lee and Kong [4] that says for any odd \(n \geq 3\), the \(n\)-star \(St(a_1, a_2, \ldots, a_n)\) is super edge magic. We solve the two cases:

1. The \(n\)-star \(St(a_1, a_2, \ldots, a_n)\) is super edge magic where \(a_i = 1 + (i – 1)d\) for all integers \(1 \leq i \leq n\) and \(d\) is any positive integer.

2. An \(n\)-star \(St(a_1, a_2, \ldots, a_n)\) is not super edge magic when \(a_1 = 0\).