V4- Magic Labelings of Some Wheel Related Graphs

Abstract

The Klein 4-group, denoted by V4 is an abelian group of order 4. It has elements V= {0, a, b, c}, with a + a = b + b = c + c = 0 and a + b = c, b + c = a, c + a = b. A graph G= (V (G), E(G)), with vertex set V (G) and edge set E(G), is said to be V4 magic if there exists a labeling l : E(G) → V4 \ {0} such that the induced vertex labeling l+: V (G) → V4 defined by is a constant map. If this constant is equal to a, we say that l is an a-sum V4 magic labeling of G. Any graph that admits an a- sum V4 magic labeling is called an a- magic V graph. When this constant is 0 we call G a zero-sum V4 -magic graph. We divide the class of V4 magic graphs into the following three categories:  (i) Va, the class of a-sum V4 magic graphs, (ii) V0, the class of zero-sum V4 magic graphs, (iii) Va;04, the class of graphs which are both a-sum and zero -sum V4 magic. In this paper, we identify some cycle related graphs which belong to the above categories.