LAUSR

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 μs(G), is the minimum nonnegative integer n such that G ∪ nK1 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 Dn for n ≡ 0 (mod 4). We also give an exact value of super edge-magic deficiency for a ladder Pn × K2 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 Pn for n ≥ 3.