On the dimension of vertex labeling of $k$ -uniform dcsl of an even cycle

Abstract

In this paper, we discuss the lower bound for the dcsl index δk of a k -uniform dcsl of even cycle $C_{2n}$, n ≥ 2 , in terms of the dimension of a poset and prove that dim($mathscr{F}$ ) ≤ δk (C2n) , where $mathscr{F}$ is the range of any k -uniform dcsl $f$ of $C_{2n}$, n ≥ 2 .