Super Edge-Magic Total Labeling of Subdivision of Stars

Abstract

An edge-magic total \((EMT)\) labeling on a graph \(G\) is
a one-to-one mapping \(\lambda : V(G) \cup E(G) \to {1,2,—,|V(G)| +
|E(G)|}\) such that the set of edge weights is one point set, i.e. for
any edge \(xy \in G, w(xy) = {a}\) where \(a = \lambda(x) + \lambda(y) + \lambda(xy)\)
is called a magic constant. If \(\lambda(V(G)) = {1,2,—,|V(G|}\) then an
edge-magic total labeling is called a super edge-magic total labeling.
In this paper, we formulate a super edge-magic total labeling for
a particular tree family called subdivided star \(T(l_1,l_2,\ldots,l_p)\) for
\(p>3\).