Most wheel related graphs are not vertex magic

Abstract

Suppose G is a finite graph with vertex-set V(G) and edge-set E(G). A one-to-one map λ from V(G) ∪ E(G) onto the integers 1,2,3,..., |V(G)| + |E(G)| is called a vertex-magic total labeling, if there exists a constant h so that for every vertex x, λ(x) + Σλ(xy) = h where the sum is taken over all vertices y adjacent to x. The constant h is called the magic constant for λ. A graph with a vertex-magic total labeling will be called vertex-magic. In this paper, we consider the vertex-magic total labeling of wheel related graphs such as Jahangir graphs, helms, webs, flower graphs and sunflower graphs.