Publications

Abstract : A (p, q)-graph G is known as super edge-magic if there exists a bijection f from V (G) ∪ E(G) to {1, …, p + q} in such a way that, for any edge uv of G, f (u) + f (v) + f (uv) = c f, is a constant and f (v) ∈ {1, …, p}. Such an f is called a super edge-magic labeling of G and c f is called the super edge-magic constant of G. The strength of a super edge-magic graph G is the minimum of all such c f ’s where the minimum is taken over all super edge-magic labeling f of G. If G is a (p, q)-super edge-magic graph, then we have that q ≤ 2p − 3. Further, any super edge-magic graph G is maximal if q = 2p − 3. In this paper, we give a characterization for any connected triangle-free graph G to attain the lower bound of its super edge-magic strength. Moreover, we determine the strength of certain well-known classes of maximal super edge-magic graphs with girth less than 4.