Non-existence of skolem mean labeling for four star graphs

Abstract

In this paper, we prove if $r > s < t$, the four star $G=k_{1,r} \cup k_{1,r} \cup k_{1,s} \cup k_{1,t}$ is not a skolem mean graph if $\left|s-t\right| > 4 + 2r$ for $r = 2,3\cdots$; $s = 1,2\cdots$ and $t \geq 2r + s + 5$.