### Some Results on Super Edge-Magic Deficiency of Graphs

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**Authors:**M. IMRAN, A. Q. BAIG AND A. S. FENOVCíKOVá

**DOI:**10.46793/KgJMat2002.237I

**Abstract:**

An edge-magic total labeling of a graph G is a bijection f : V (G) ∪ E(G) →{1, 2,…,|V (G)| + |E(G)|}, where there exists a constant k such that f(u) + f(uv) + f(v) = k, for every edge uv ∈ E(G). Moreover, if the vertices are labeled with the numbers 1, 2,…,|V (G)| such a labeling is called a super edge-magic total labeling. The super edge-magic deﬁciency of a graph G, denoted by μ

_{s}(G), is the minimum nonnegative integer n such that G∪nK

_{1}has a super edge-magic total labeling or is deﬁned to be ∞ if there exists no such n.

In this paper we study the super edge-magic deﬁciencies of two types of
snake graph and a prism graph D_{n} for n ≡ 0 (mod 4). We also give an
exact value of super edge-magic deﬁciency for a ladder P_{n} × K_{2} with 1
pendant edge attached at each vertex of the ladder, for n odd, and an exact
value of super edge-magic deﬁciency for a square of a path P_{n} for
n ≥ 3.

**Keywords:**

Super edge-magic total labeling, super edge-magic deﬁciency, block graph, snake graph, prism, corona of graphs, square of graph.

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