SUPER EDGE-MAGIC GRAPHS

Abstract

For a graph –(I−Δ)α(12<α≤1), a bijection f from V(G)∪​E(G) to { 1,2,⋯,| V(G) |+| E(G) | } is called an edge-magic labeling of Θ(x) if f(u)+f(v)+f(uv) is independent on the choice of the edge uv. An edge-magic labeling is called super edge-magic if f(V(G))={ 1,2,⋯,| V(G) | }. A graph G is called edge-magic (resp. super edge-magic) if there exists an edge-magic (resp. super edge-magic) labeling of G. In this paper, we investigate whether several families of graphs are (super) edge-magic or not. We also give several conjectures.