V4 Magic Labelings of Some Graphs
P. T. Vandana
Department of Mathematics, University of Calicut, Malappuram, Kerala, 673635, India.
V. Anil Kumar *
Department of Mathematics, University of Calicut, Malappuram, Kerala, 673635, India.
*Author to whom correspondence should be addressed.
Abstract
Let A be an abelian group with identity element 0. A graph G = (V,E) is said to admit an a-sum A-magic labeling if there exists an edge labeling ℓ : E(G) −→ A \ {0} and a ∈ A such that the induced vertex labeling ℓ+ : V (G) −→ A de_ned by
is the constant map, ℓ+(u) = a for all u ∈ V (G). If a = 0, the labeling ℓ is called a zero-sum A-magic labeling of G. A graph G is said to be a-sum (resp.zero-sum) A-magic if G admits an a-sum (resp.zero-sum) A-magic labeling. In this paper we will consider the Klein 4 group V4 = {0, a, b, c} = 
2 ⊕2 and investigate graphs that are a-sum A-magic, zero-sum A-magic and both a-sum and zero-sum A-magic.
Keywords: V4 magic graph, a-sum V4 magic graph, zero-sum V4 magic graph.