Some results on super edge-magic deficiency of graphs

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 D_n for n ≡ 0 (mod 4). We also give an exact value of super edge-magic deficiency for a ladder P_n x 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.