On super vertex-magic labeling

Abstract

For a graph G(V, E) an injective mapping f from V ⋃ E to the set {1, 2, 3, …, v + ε} is a vertex-magic total labeling if there is a constant h so that for every vertex v ∈ V, f (v) + Σ f (uv) = h where the sum runs over all vertices u adjacent to v. A vertex-magic labeling f is called super vertex-magic labeling if f (E) = {1, 2, 3, …, ε} and f (V) = {ε + 1, ε + 2, …, ε + v}. A graph G is called a super vertex-magic if there exists a super vertex-magic labeling of G. In this paper, we established some properties of super vertex magic trees and exhibit super vertex-magic labeling of a kite graph.