Non Existence of Skolem Mean Labeling for Eight Star Graph

Abstract

In this paper, we prove if $\ell\leq m < n$, the eight star $G=K_{1,\ell} \cup K_{1,\ell} \cup K_{1,\ell} \cup K_{1,\ell} \cup K_{1,\ell} \cup K_{1,\ell} \cup K_{1,m} \cup K_{1,n} $ is not a skolem mean graph if $\left|m - n\right| > 4 + 6\ell$ for $\ell=2, 3, . . .$ ; $m=2, 3, . . .$.