Abstract: In this paper, we introduce a new type of labeling called relaxed Skolem
mean labeling. We prove, if is
not a relaxed Skolem mean graph, the two stars is a relaxed Skolem mean graph if and only if the
three stars is
a relaxed Skolem mean graph if for
the
three stars is a relaxed Skolem mean graph if for
and
any path is a relaxed Skolem mean graph. Also, we prove the relaxed Skolem mean
labelings are linearly independent from the Skolem mean labeling.
Keywords and phrases: Skolem mean graph, relaxed Skolem mean graph, path and star.
