V4- Magic Labelings of Some Shell Related Graphs
V. Anil Kumar *
Department of Mathematics, University of Calicut, Malappuram, Kerala- 673 635, India.
P. T. Vandana
Department of Mathematics, University of Calicut, Malappuram, Kerala- 673 635, India.
*Author to whom correspondence should be addressed.
Abstract
For any abelian group A, a graph G = (V;E) is said to be A-magic if there exists a labeling ` : E(G) ! A n f0g such that the induced vertex set labeling `+ : V (G) ! A defined by
is a constant map. A graph G = (V, E) is said to be a-sum A magic if there there exists an a 2 A such that `+(v) = a for all v ∈ V . In particular, if a is the identity element 0, we say that G is zero-sum A magic. In this paper we will consider the Klein-four group V4 = {0; a; b; c} and investigate a class of V4 magic shell related graphs that belongs to the following categories:
(i) Va, the class of a-sum V4 magic graphs,
(ii) V0, the class of zero-sum V4 magic graphs,
(iii) Va, 0, the class of graphs which are both a-sum and zero -sum V4 magic
Keywords: Klein 4-group, V4- magic graph, Shell graph, multiple shell, umbrella graph.